Good evening,
I will begin by acknowledging the fact that the Sims 2 lacks traits such as "insane" that are present in latter iterations, and I am trying to adapt to this. Anyways, how do you guys create eccentric/ off-kilter sims? Are such qualities based on preferences (sim-wise) or personality points-or perhaps a mixture? I genuinely need advice on creating them, in order to "spice" up my game.
Thank you fellow simmers- you're the best!

I usually write down something to describe the personality a sim has, and when that is not enough, I give them weird faces and/or extreme personalities. For example, an extremely outgoing sim will enter hot tubs naked, and a playful one can act in a somewhat childish way. You have to play them in the way you want them to be though,but that is the way I make many of my sims. I once created a sim with an extreme personality, and when she went to college, the amounts of drama she caused were astronomical because she took decisions on a whim, and let me tell you, she is one of my favorite sims in my neighborhood.

If you want a sim to be crazy just let their aspiration drop and they will start doing insane things. Rocking a flour sack baby or talking to a ball. Make them very outgoing and they will hot tub naked, add in the choose to go naked mod and they will wonder around at times naked. Make them very messy and you will see them eat from your rubbish bin, make them have no nice points and they will end up poking and fighting other sims. Also don't forget the interest panel, in SimPE you could make them have full points on aliens and zero on normal topics. So pretty much all they want to talk on is aliens.

Sims 2 sims don't need traits because they have personalities.

(Rubs hands together.)
Extreme personalities and appearances are good and will help you along, but the simplest way to get an eccentric sim is to have an eccentric ruleset.

The obvious example here is Bad News Bev. Bev is the Tricou with the Nightlife Hair, so - too pretty by half, unremarkable point spread. But I gave her a rule - no locking of wants, fill as many wants as possible - favoring the high point ones - without regard to consequences. This includes Trying for Baby if the birth control is up to h er, because she cannot remember to use it correctly if her partner's not on top of it. If she's already platinum, free-range her. So, drama, drama, all around, nor ever stop to think! But she's actually a pretty good mother (and a good thing, too, since she's got three kids from three different fathers), and it turns out her husband has a kink and likes knowing that his wife gets around, and one of her brothers is profoundly devoted to her. She's into art, and I tell her to do weirdass custom paintings; and she likes buying clothes, so she has closets full of clothes nobody else would dream of wearing.

Bad News Bev's ruleset was a result of my realizing that I hadn't mastered playing Pleasure sims and experimenting. You could do something arbitrary like that; or you can make a backstory in CAS and make a ruleset based on it. Give characters tragedies (sole survivor of the accident that killed the rest of the family), medical conditions (on the autism spectrum, dyslexic, heart disease), or family traditions (We've always been clowns, son, what's this doctor nonsense?) and make rules limiting certain behaviors and encouraging others to reflect them. If a sim can't read in order to skill, or isn't allowed to Work for the Man, or has to follow a certain routine even when that routine interferes with his life and well-being, that sim will have challenges and opportunities, and will develop a character, that is different from your mainstream sims, while you're playing him. Then, when you see him in uncontrolled situations - in the background of community lots, for example - you'll find yourself interpreting his behavior in terms of the established idiosyncrasies of the character, and he'll start getting depth and character growth.

You could look at their personality points and develop some eccentric traits
-A neat freak sim you wake up middle of the night to go on cleaning sprees because they can't stand the thought of anything in the house being dirty, if they go back to sleep they will have nightmares about it.
-Sims who are lazy or super shy could be actually just afraid to leave the house so they work from home, have everything delivered, and refuse to go on outings, even if they roll wants to because their fear of the outside world keeps them in the home.
-Have hoarder sims, like whenever you want to buy something new, you can't throw the old thing away, and just keep on arranging furniture, sticking old/broken items in the attic until they can't function.
-Playful Prankster sims who can't help but to prank everyone they meet. I can't imagine they would have a lot of friends that way, unless they quickly apologized and got into a good conversation.

Just a few thoughts.

And that is what I did with the sim I was talking about. She comes from an extremely authoritary family, but she always takes decisions based in what she thinks it's okay. She wants a makeover? She gets it. Someone dissaproves of her? That someone becomes her enemy. She is also really unstable, attacking people for no reason, and I never stop her when she does something stupid. The best thing? Her fiance likes, or better said, LOVES the way she is, so he started acting just as spontaneously as her, and that is the main reason I love that sim so much, because her character is well defined, and manages to stand out from other sims.

I probably would utilize the "Asylum" concept, where I would leave my insane sim to roam around without my commands (unless I have do to something big that would lead them to another life path that follows the direction of a storyline), because sims are pretty much crazy on their own when left alone to do the decisions.

I think my Mr No Nice Points (born in game) may qualify - he likes beating other Sims up. And he has all his body skill points now, so he beats them up properly Because he has 6 playful points, a pillow fight may take place with a friend to celebrate his latest win in a street/ bar fight. That sounds insane Yet his reputation is going up, he has a small group of loyal friends, and I am rather fond of him. Because Sims 2, as Jo points out, are much more than a combination of silly traits.

I think that another good idea about making a sim look eccentric is to make they do things different than usual. For example, a firefighter in Circadian Springs (my custom 'hood) is supossed to be a little "crazy" and, as his OTH is nature, instead of sleeping inside the building like the other firefighters, he sleep in a tent on the roof of the fire station near his plants and he can only sleep there. Just that already making him look odd in comparsion to others.

About extreme personality points, making a sim extremely shy (0 or 1 outgoing points) can also works, as they will be very socially awkward in general.

Amazing suggestions! I will most certainly implement them!
-P.S. The "Insane" trait in Sims 4 wasn't all that interesting, anyways...

I usually don't even have to decide which traits they have - they're usually quite happy to tell me; I just have to pay attention when I'm playing them.

I've always thought that the "Grilled Cheese" Aspiration was a bit on the loony side too. I mean, really? All a pixel ever thinks about is grilled cheese? That's an obsession-not healthy either. They get fat from eating those sandwiches without ever dieting or exercising..
But in other cases-working against a personality will also cause a pixel to act a bit weird. For example: if they have a shy/reticent personality, making them a popularity aspiration will push them to the brink when they're not feeling like it..and so on.

It's called going against type and sometimes it works.

Or super shy + romance aspiration or super playful + knowledge.

Guess what guys! I made a really- actually crazy sim! He had Very High playful and active points, and low nice points, so he would switch mood constantly. He also laughed a lot, for no apparent reason! Thanks a lot for your help!

Lol, nobody likes my comment! :/

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Hobbies can be another way to play sims in unique ways - not only can sims have different hobbies, but how they practice those hobbies can be different. A nature sim might love gardening, or fishing, or bird watching, or hiking; a sports sim might view their sports memorabilia, watch sports, or play a specific sport; a music and dance sim might only play one instrument, or do ballet, or dance at night clubs....

I find the hobby wants are fairly easy to train sims to frequently reroll, so it's quick to turn a sim into an obsessive hobbyist. I've had a few in the past that I really played to their hobbies - the jogger that had to have at least one run a day (I wouldn't direct her to do anything else until that want was filled, and if she didn't run she was left to autonomous control), and the one that spent most of her leisure time bird watching and had pet birds and bird deco were probably my most eccentric hobbyists. The other sims weren't very eccentric, but the hobbies helped flush out their personalities and differentiate them from others in my 'hood.

I imagine running 7 restaurants (is there any limit to how many lots one can purchase?) would be kinda on some level eccentric for Cuisine hooked sims.

You could even have the sim be crazy over something that they have high with the respective [url=http://sims.wikia.com/wiki/Interest]interest.
E.g, workaholic freak that's interect in jobs. Died hard sport fans that like sports. Have those who are interested in paranormal become every possible occult through their life have them commit lots homicides just to get a chance to study grim reaper physiology and background. Crazy cat lady who likes animals.... There are lot of things you can think of by utilizing the Interest concept. Just go wild with your imagination.

I have a Sim with Knowledge as primary aspiration & Grilled Cheese as secondary. Two aspirations arguing with one another for dominance can be highly entertaining.

I made a grilled cheese sim once- He was pretty insane but got boring real quick. In real life, I would be a Knowledge/Wealth/Cheesecake/Ice-cream aspiration
@SneakyWingPheonix
I think the sim would go crazy from managing all those restaurants- I know I would... Unless they sold my favorite food, of course! Helpful advice though.

And Family/Romance is all kinds of fun!

Romance/family. Constantly wanting to get engaged to every new lover (disregarding the fact that they're already engaged) while simultaneously fearing it. Wanting kids but fearing having them. Sure, I sometimes play that just as someone who realizes starting a family is a Really Big Deal and will change your life forever, but it can also be interpreted as more on the crazy side. Grilled cheese is a simple obsession, but can be either an escape mechanism, or something they try to force on everyone around them. A fortune sim with no nice points can be a psychopath/sociopath who will steamroll their way over everyone around them if given half a chance.

Maxed Nice sims can make an astonishing number of enemies if you give them free reins, because they'll walk up to complete strangers and try to hug them, which will often not be appreciated. Combine it with maxed Outgoing, which will make them walk into people's homes without being invited, and it could get really interesting. (Zero or maxed Playful can add to that further.) Likewise, for a recluse with OCD, start with maxed Neat and no Outgoing points.

But just in general, take your hands off the mouse/keyboard and watch what they do. Spend hours staring out the window looking worried? Paranoia. Spend the whole night at some activity, only to crash and burn in the morning right when they should be going to work/school? Should have social consequences. Jumping in puddles in the middle of a storm? Potentially suicidal risk-taking behavior. Keep track of what wants they roll up, then take a look at their interests, and see if the whole picture might start to come together...

I don't set out to make my Sims eccentric. They just come out that way.

Probably they get it from me!

I play lots of aliens, and always do Boolprop so I can change their interests and personality to extremes; what I have found is that if a Sim has only 1 (or less) trait, their kids will have LOTS! As, my Brandy Broke has zero clean points, her kids have 5 or more. Extreme interests can make them social failures (like Nervous - who has no interest in anything, and no personality except active).