Would you consider Jensen being something of a Big Bang Theory character as "weird" and "maladjusted" enough? If so, you HAVE to read Your brains are no match for my tractor-beam (http://longsufferingly.livejournal.com/10691.html). It's really cute and fun, so maybe it's not dark enough for you?
But it's just so good :-)

I second this rec!!!

I love this one! I'm not necessarily looking for dark, just quirky, and that fits the bill pretty darn perfectly as far as BBT!jensen being weird-ish, not shy. Feel free to throw anything else you've got like that my way :)

I recognize The Puzzle That is Me as belonging to felisblanco and I'm going to assume if you read that piece from her, you must have also read The Doors of Time (http://felisblanco.livejournal.com/1090487.html), her masterpiece in my opinion. But for some reason, you hadn't, I think it might fit into the 'socially awkward' category.

This one has an antisocial Jensen in it and j2 meet in extremely unusual circumstances. I'm not sure you like these types of stories but I found it entertaining and different.
Reanimated (https://archiveofourown.org/works/151617)
summary: In which Jared manages real estate in Heaven and Jensen works as Hell’s attorney in Death Trials. Extreme ambiguity and a distinct lack of beer push Jared to accept a different kind of job in a hotter, more southern locale. The boys meet. Hi-jinks and grocery-stealing in Hell ensue. Featuring saints on book tours, love on trial, after-life bureaucracy, and sin. Surprisingly not as cracktastic as it sounds.

This is also in a weird setting. Talking Through a Different Face (https://archiveofourown.org/works/229144)
summary: When single dad Jared Padalecki is recruited under desperate circumstances to become the “normal” face of a house full of misfits (including a vampire, a voodoo priestess, a man who has modified his body to look like a jungle cat, and an all-too-naked Misha Collins) he unwittingly enters a world where magic exists. He thinks his greatest problem is figuring out his surprising attraction to Jensen “Totally Not a Warlock” Ackles, but when his suddenly super-powered six-year-old daughter goes missing, he needs to learn to trust his newfound family to get her back before anyone else is harmed.

antisocial!Jensen Monster (http://redrum669.livejournal.com/7862.html) by redrum669
summary: Jensen lives a reclusive life and acts like a jerk for a reason. Jared sees his chance in uncovering it when tutor sessions born of desperation give him the opportunity to talk to Jensen in private. When he falls for Jensen, though, secrets of the past don't seem all that important anymore. That is until life-altering news have Jared wondering if there's more to the proverbial skeleton in Jensen's closet than he ever thought.

awkward!Jared Disaster. (This is a Good One.) (http://aisalynn.livejournal.com/120738.html) aisalynn
summary: Jared, a college drop-out, unlucky in love and a self-professed "loser" finds himself at the end of his rope. His boyfriend, Misha, has ditched him at the last moment, right before the family Christmas dinner Jared'd planned to bring him to, and thanks to an untimely phone call from his mother, Jared's family thinks Misha is still coming.

A series of uncomfortable moments later--including awkward phone calls to his exes, a terrible trip to the mall with is best friend where they were escorted out by security, and a run in with a schizophrenic who thought Jared was trying to take him into a secret government lab--and Jared has Jensen--an angry, former lawyer who's dedicated his life to charity work--handcuffed in his car, blackmailed and forced into pretending to be Jared's boyfriend. As the holiday stretches on and the charade he's involved in becomes less and less a lie, Jared is only sure of one thing: he should stop listening to Chad.

weird/feral!Jensen Beholder (http://sandymg.livejournal.com/37314.html?format=light&page=2) by sandymg
summary: Jared was passionate about the work he did with the animal shelter. Between that and living with Sandy, life was satisfactory. Until the cold night that the filthy, homeless man hidden in an oversized hoodie was dumped at the shelter and Jared couldn't just turn him out. Even if the man roared and called himself 'Beast.' Because under the hood, Jared was sure he caught a glimpse of a prince in those green eyes.

antisocial!Jensen Sound Perception (http://rocketslash.livejournal.com/?skip=10) by rocketslash
summary: Jared’s life has never been complicated. He flies by the seat of his pants and makes the best of whatever he gets. Jensen lives a reclusive and controlled life. Not by choice, but borne out of necessity. When their worlds collide, it isn’t pretty but somehow they make it work. When Jensen’s past catches up with him, nothing is certain anymore. With the odds stacked against them, can they find their way back to one another or did they even know who each other really was to begin with?

this is more weird!misha, closed off/antisocial!jared, and weird circumstances. Drifting Through Doorways (http://archiveofourown.org/works/850488/chapters/1625888)
summary: One year ago, Jared lost his husband in an act of senseless violence. Stricken with grief, Jared has withdrawn from society and become reclusive, his only human interaction coming from his foster brother Chad, his florist friend Misha, and the occasional grocery store cashier – that is, when Chad can convince him to leave his apartment. If that wasn’t bad enough, now he’s being haunted by the ghost of his deceased husband, and Misha is the only one who seems to believe him – even if Misha's theories and superstitions make him a little, well, eccentric. Jensen, on the other hand, is finally free of his own unhealthy relationship. Too bad being one half of the couple known as Jen-Jen drove him completely bat-shit crazy. And he is, if the disembodied voice that only he can hear and strange dreams are any indication. After all, Jensen is ninety-nine percent sure he’s not a ghost (despite what the voice claims), and he’s never been married to anyone named Jared, either. This is a story about unlikely connections, second chances at love, and giving in and letting yourself be just a little bit crazy.

I had to split it off because of the word count limit. =(

Anyways I hope there are a few recs you'll enjoy here.

Edit: Here's another.
Jensen and Jared are both kind of mean and stuck up here. Bratty Little Bastards: Autumn (http://archiveofourown.org/works/914322/chapters/1772560)
summary: Jensen Ackles hates coming in second. Jared Padalecki can’t stand being overlooked. So when the same guy makes them look like chumps by taking over the varsity lacrosse team and ranking first in the junior class at the private, elite Eldridge Academy, overachieving computer genius Jensen and popular athlete Jared decide to put aside their differences. Kind of.

Talk Hard (http://sandymg.livejournal.com/31061.html) by sandymg
verse summary: Jared is a struggling grad student working a phone sex line to get by. Jensen is a recluse genius doing top-secret decryption for the Defense Department. Sometimes it's not about the words, but the silence between them.

Edited 2014-05-04 07:07 pm (UTC)

I've read half your recs before but haven't heard of the other half, so I'm very excited, and I'll hop right on that! I have actually NOT read the Doors of Time, shame on me, but I have meant to forever and ever. If you've got any more recs on this theme or just a general recs list of your own floating around somewhere, I'd love a link.

I really should put the links to the recs more permanently on my livejournal or make a delicious account.
Yes I believe I remembered a few more along this line.

Slow is Smooth (and Smooth is Steady) (http://www.mediafire.com/view/?abd28ov5j94737m) by splashpink has bodyguard!Jensen who acts kinda a jerk/antisocial.

Stained Glass Masquerade (http://www.mediafire.com/view/p1gw9d71x8epgb6/Stained_Glass_Masquerade_and_timestamp_by_splashpink.pdf) also by splashpink
Basically it's a Dollhouse AU, with Jensen as a 'doll' and Jared as his 'handler'.

Jensen is very indifferent about his job here and Jared tries to understand him. Do I seem Bulletproof to you? (http://fleshflutter.livejournal.com/43577.html) by fleshflutter
summary: When he can't find any acting work, Jared takes a job as driver and bodyguard to Jensen, who is an extremely expensive prostitute with a bad habit of attracting crazy people.

Half Truths and Lies (http://rocketslash.livejournal.com/21359.html) by rocketslash
summary: A bitter and distrustful former television journalist, forced out of a job that he loved and defined him is in search of some sort of revenge by writing his memoirs. His agent sets him up with a co author who is a former democratic speech writer and once rising PR star that disappeared from politics without explanation almost two years ago. Both men have secrets; both have reasons not to trust, but writing a book together means they have to learn to get past the anger and hurt and find a way to work together. It's not easy. It's not pretty. And sometimes it's just flat out dangerous. Bit by bit cracks start to appear in the walls they've built to protect themselves and they're shocked to discover the growing feelings they have for each other. When the secrets start to be unearthed and threaten to damage one or both of them, they have to find something deep within themselves to love before they can begin to love and protect someone else.

Counting the Steps to the Door of Your Heart (http://annella.livejournal.com/1061203.html) by annella
summary: Jensen's life isn't perfect, but he's happy enough. He has friends (well, one friend and one roommate), a prospective career (if he can pass this stupid, stupid test which requires him to be able to talk to people), a sex life of sorts (with guys who are total jerkfaces and think Jensen is a dork, which is actually true), and a life-size Dalek costume with a voice modulator which lets him EXTERMINATE things (like the toaster). Then, out of nowhere, he also has Jared (gorgeous, wonderful, socially retarded, and already taken), and his life turns upside down in the blink of an eye. For the first time, Jensen has found what he wants, but how is he going to get it?

Short one shot with shy!Jensen They Say I'm a Dreamer (https://archiveofourown.org/works/470065)
summary: In which Jensen's kind of a shy tool and his coworkers are totally sick of him failing to talk to the hot guy in the elevator.

Your Princess Is in Another Castle (https://archiveofourown.org/works/682253)
summary: It's not easy being a video game Bad Guy. Luckily, Jared is awesome and everyone likes him anyway. Now all he has to do is convince the attractive, antisocial Good Guy from the arcade's newest First Person Shooter that being a Bad Guy isn't a bad thing. And that they should totally date.

Those two above recs were from cleflink (https://archiveofourown.org/users/cleflink/pseuds/cleflink).

Manufacture a Miracle (https://archiveofourown.org/works/298188)
summary: Jensen and Jared are fic writers who take their rivalry very seriously--well, as seriously as a show about a zombie apocalypse can get. But when they imprint-at-first-sight while at a fandom convention, Jensen has to battle horny TV stars, physical exhaustion, and the loss of his favorite shoe to convince his brain what his body already knows--that Jared is his soulmate.

Also if you haven't already checked out the SPN Big Bang (http://spn-j2-bigbang.livejournal.com/) list, you should do that! They organize it by RPS/SPN fics and slash and they give out the summaries.

Edited 2014-05-05 05:13 am (UTC)

It's a little disconcerting to realize how close your taste and mine in fanfic seem to be! If you post a Recs list, I would absolutely be interested in seeing it! Thanks so much for sharing all these, several of which I haven't read.

Oh well I'm really glad you enjoy the recs I have up here. =)

Man in the Water (http://morrezela.livejournal.com/4738.html) by morrezela
Summary: From the spnkink_meme Prompt: “Jared has taken to waking up really early in the morning so that he can get a prime spot - every morning he spies on Jensen who swims/baths in the lake in forest. Jared thinks that Jensen is beautiful, but he, Jared, is too shy to talk to him. Jared has taken to leaving little tokens for Jensen to find - a carving, flowers, a fluffy towel - anything he can think of to get Jensen to smile.”

Um, not actually very creepy.

Not creepy is ok! When I said creepy I meant more like "ha ha, you creepster" more than actual dark!fic. Your rec sounds excellent :)

he Instant Message (http://bedtime-stories.livejournal.com/124367.html)
A miss-sent Instant Message begins a flirtation that soon could turn into something more. That is, if Jared will come out from behind the computer an let Jensen see the real him.

Given and Taken in Ink (http://marishna.livejournal.com/561865.html)
Author Jared Padalecki has created a sheltered existence for himself, believing that he's happy half-living his safe life. He hides behind his pen name so few people know the real Jared, as he protects himself from others finding out his books aren't 100% fiction. His new neighbour, Jensen Ackles, knows there's something different about Jared and pushes until he has no choice but to let Jensen in. When Jared's carefully constructed life collapses around him will Jensen even care who Jared really is or will Jared's worries become reality?

Somebody made you smile into their lens (http://icebear-cw.livejournal.com/17825.html)
Jared Padalecki loves to spend his time buried in books. Jensen Ackles is the photographer everybody wants to hire. They are polar opposites but neither of them can help being drawn to one another whenever they meet - and Jensen doesn't even believe in fate. So Jensen doesn’t really get why fate insist on throwing them together over and over again when it’s not him being crazy over the geek but Chris.

Run 'Verse (http://beckalooby.livejournal.com/30878.html)
No one likes Jared because he’s different, he runs away from the scary world before it can catch up and hurt him more than it already has. One day he meets a man who gets him to slow down.

Going Undercover (http://annie-46fic.livejournal.com/252050.html)
Jensen is a CEO who wants to believe all of his employees are treated well. He goes undercover as a trainee to find out just what does go on in his offices and gets a shock when he meets shy mailroom clerk Jared. What will Jensen do when he discovers just how badly Jared is treated and how is Jared going to react when he finds out that JR his new trainee is actually the CEO he has a huge crush on?

Gifted and Talented (http://dimeliora.livejournal.com/43871.html)
Jared, a world-renowned chess player and huge geek, meets Jensen Ackles the boxer. Sparks fly, but Jared learns that being gifted and talented in academic pursuits means nothing in love

Out of Silence (http://annie-46fic.livejournal.com/56867.html)
When hardened, but lonely cop, Jensen Ackles meets Jared Padalecki in his family’s diner, he doesn’t realise that his life is about to change drastically. Jared is a complete innocent, deaf, mute and unable to communicate, he needs a friend. Can Jensen be that man?

Like a Detuned Radio (http://homo-pink.livejournal.com/47384.html)
When Jared's released from prison, Jensen is there to help him cope. Parole officer/ex-con AU

xxx

A Day For The Beach (http://brutti-ma-buoni.livejournal.com/414043.html)
Jensen's been closed off for a long time. He doesn't meet people, he doesn't have friends, he doesn't have music. He doesn't need any of that. But some determined neighbours start to change the way he feels, by means of cunning and cats. And then he meets Jared, drifting through life in a way Jensen can't imagine. Can their very different lives come together?

Shelter (http://lasvegas-lights.livejournal.com/84747.html)
Jensen carries a powerful secret, one that forced him to run away from home and live a life of solitude in the forest. His only company is his dog Sadie and JD, who brings him supplies once a week. His quiet, drama free existence is shattered by Jared, a man unable to come to terms with the loss of his brother, the only family he had. Out in the woods they find each other, and it's only with each other’s help that they learn to heal, and find something neither of them expected along the way.

The Opposite of Stereo (http://archiveofourown.org/works/303341)
The bookshop on Walnut Street opens in May, and its owner is a cute, Deaf bibliophile that Jared just can't resist. But he has to work a little to bring Jensen out of his shell, and to show him that he doesn't have to be alone in his own, silent world.

Paved With Hearts (http://cjmarlowe.livejournal.com/455486.html)
Jared Padalecki has been shuffled from home to home for most of his life until one summer he's left with the black sheep of the family, his unsocial Uncle Jeff, up in the Coast Mountains of British Columbia. He unexpectedly finds a home and a family there, but when the summer's over he's torn away from it and placed with a family in the city; in return for having a good school to attend to finish his senior year, he's asked to befriend their shut-in son, a young man named Jensen who hasn't had an easy time of it either.

awkwardly flirting (http://collidefics.livejournal.com/41720.html)
Jensen's socially awkward. But he likes someone. So he'll do what he can, even if it means flirting, to get Jared to like him back.

You're Like a Parachute (http://archiveofourown.org/works/307423/chapters/491797)
Jensen lives daily with anxiety and fear and Jared, his new next door neighbor hopes to find a way through that.

Lost and Found (http://mediaville.livejournal.com/57649.html)
Jensen Ackles is a shy, overweight songwriter whose body issues have prevented him from forming any real personal connections, and at thirty, he’s still unsure of his sexuality, and still a virgin. But when he signs up for an experimental obesity research program, he meets Jared Padalecki, a stunningly sexy fitness guru who slowly but surely changes Jensen’s life.

Yoko Ono’s Got Nothing on Jensen Ackles (http://4everkizuna.livejournal.com/4494.html)
Jared Padalecki has lived the hard-rock, hard-drinking lifestyle practically since the day he left his home and his alcoholic father. Jensen Ackles has been sheltered after disease almost cut his life far too short. Can they forge a path together or will forces larger and stronger force them apart.

More Than I Deserve (http://altruisticinteg.livejournal.com/65206.html)
Years of school yard bullying has left Jensen with some emotional scars and anti-social tendencies. Jensen found purpose working as an Animal Shelter Manager and he was content living the way he was. Jensen knows from his past experiences the only love and acceptance he was going to receive was from the animals he cared for until a tall, young orthopedic surgeon by the name of Jared Padalecki walked into the animal shelter looking to adopt a dog and changed everything.

The Treat Fairy (http://bbsock.livejournal.com/1642.html)
Jensen has a crush, and when he gets nervous he bakes. He noticed that his crush - his hot tall neighbor - likes sweets, so he gives all the results of his nervousness to Jared. The fact that Jared seems to like his baking just makes Jensen even more nervous..

xxx

Thirty Steps (http://www.sinful-desire.org/archive/viewstory.php?sid=3250&warning=5)
Jensen lost his lover to hate. It made him hide away, protect himself, isolate himself. His only real connection to the outside world is through his computer and a tech support guy called Jared.

If you are looking for more you can check out my tags Shy Jared (https://delicious.com/chellexxx1/Shy!Jared) & Shy Jensen (https://delicious.com/chellexxx1/Shy!Jensen)

Happy reading
xxx

Thank you so much for the huge list! I'm familiar with a few, not so much with others. I'll be happy to check them out and your tags as well :)

Pastiche by baked

Summary: Jared’s just moved into a new apartment complex and immediately warned about his upstairs neighbor Jensen who is a bit eccentric.

http://archiveofourown.org/works/1556195?view_adult=true (http://archiveofourown.org/works/1556195?view_adult=true)

I'm in the process of reading this one right now and so far I'm really enjoying it. Jensen is somewhat weird and anti-social.

Thanks!

The Trip-Hop!Verse by minchout, available on AO3
(Jensen is bipolar.)

My Last Date with You by homo_pink, also on AO3
(Jensen is obsessive and an extreme introvert)

The Sinister Nature of Cul De Sacs by fahrbot
http://iminurface.livejournal.com/7583.html
(Jared is an agoraphobe who never leaves his house.)

Hope these fit your criteria!

Haven't read the first two, LOVE LOVE LOVE the third one. Thanks for the recs :)