I've been working on several villains for my D&D campaigns, but I've begun working on another type of villain I haven't found in any book. Inspired by Carrie from the book of the same name, and Lucy from the infamous anime "Elfen Lied", this villainess is also a teenage girl who suffered the worst kind of bullying you could imagine. But that means nothing now, because like Carrie and Lucy, she too, has telekinesis(Implied to be a "gift" from one of the Evil Gods of the universe I'm building), and can tear apart anyone she doesn't like, and I want her to be the villainess in one of my campaigns. But I've never found anything in D&D about characters with telekinesis. Does anyone know what the limit of telekenisis should be? What should her level be? And how can my players fight her?

You could have a look at the Unearthed Arcana Psion/Mystic class

http://dnd.wizards.com/articles/unearthed-arcana/mystic-class

It covers telekinesis. Otherwise maybe look  through the spell lists and build a caster with suitable spells. There is a 5th level spell that is literally Telekinesis.

There is a spell called telekinesis, also consider spells like Bigby's hand, catapult and levitate. Adding some environmental aspects to a big fight that can be used as spell effects could be fun. A meeting in an old abbatoir could feature a pile of old, rusted blades that are picked up and used psychically as a cloud of daggers spell; or a tangle of ropes being used as an entanglement could really sell the opponent as psychic, rather than magical. Limits on her power are hard to set, because ultimately we don't know your party's level, play style or classes. But the limit should be broadly at the same level as your PCs, or ever so slightly over.

As for origin, I can't inform you of your own world. Personally, a hag granting these powers, or a mishap during a covert ceremorphosis by some crafty Illithids. Maybe even someone touched by the Far Realms... I do feel like such a character could do well in a Cthulu inspired lovecraftian plot.

I do hope this helps, and enjoy your game.

Well, Illthids don't exist in this world. As for players, this villainess is one of several big bads I've created. I just need to sort them into challenge rates, the weaker ones will be the first ones faced. Stronger ones will be faced later once the players are stronger and at higher levels. But it sounds like this villain could be put anywhere on the order of story villains. Even though I'm bringing in my own geography, history, and even gods to this world, it does have the same races, magic spells, and all other gameplay features.

The closest thing to what you want is a Githzerai Anarch. In short, you want a creature that has an Innate Spellcasting (Psionics) that allows them to cast certain spells without requiring any components. Spells like Mage Hand, Shield, Levitate, Arcane Hand, Telekinesis and Psychic Scream are good fits. Another neat hack is to make those spell effects invisible. The playable Gith race's Mage Hand effect is invisible when they cast it using their psionics racial trait.

If she's going to fight the party alone, you'll want to give her Legendary Actions and possibly Legendary Resistance.

Don't be afraid to steal traits and attacks from other monsters, like Mind Flayers or Star Spawn. Reuse as many of the game's existing building blocks as you can get away with before trying to design and balance something from scratch.

 I see. Thanks.  I'll use the Anarch states, but the character herself is a human with supernatural abilities. She's based on Carrie and Lucy from "Carrie" and "Elfen Lied."

If you don't have the slightest clue where to start with monster stats, the DMG has good baseline stats for each CR. But don't be afraid to course correct mid-battle. You might design your villain with 100 hit points, then realize 2 rounds in that the fight is going to be way too short, and bump that up to 150. The players can't tell the difference. The important thing is to match the player's expectations and deliver a satisfying experience.

You’re the DM, so you can do anything. But if I I was creating that as a player I’d create a Warlock with Mage Hand, Unseen Servant, Catapult, Gust of Wind, Levitate, Erupting Earth, Black Tentacles, Arcane Hand, and Telekinesis on its spell list. 

Quote from InquisitiveCoder >>

The closest thing to what you want is a Githzerai Anarch. In short, you want a creature that has an Innate Spellcasting (Psionics) that allows them to cast certain spells without requiring any components. Spells like Mage Hand, Shield, Levitate, Arcane Hand, Telekinesis and Psychic Scream are good fits. Another neat hack is to make those spell effects invisible. The playable Gith race's Mage Hand effect is invisible when they cast it using their psionics racial trait.

If she's going to fight the party alone, you'll want to give her Legendary Actions and possibly Legendary Resistance.

Don't be afraid to steal traits and attacks from other monsters, like Mind Flayers or Star Spawn. Reuse as many of the game's existing building blocks as you can get away with before trying to design and balance something from scratch.

It might also be easier for a main villain if you don't try to give her specific numbers of uses of these powers too. If you think 'at will and unlimited' is too powerful (you may not), then it might be easier for you to go with a Warlock sort of spell slot system for her. She has a list of powers, she has X number of slots she can cast, and that's that.

You might also change it by making it more of a Spell Points sort of system. She has X number of Total Spell Levels she can cast, and you subtract the spell level of each spell as you cast it, but you can cast whatever spell you want as long as you have the points.