2) Usually refers to girls who are interested in computers, and technology in general, can also be used for girls who do things not considered "cool" by everyone else.
3) A compliment to girls who are proud to be geeks.
Person 2: Oh, that's our resident geek girl.
Person 1: Well, we've got jocks, preps, nerds, burnouts, and a few geek girls hanging out in the library.
These chicks are smart and sassy and totally make "geek" look sexy!
Geek girls enjoy logo t-shirts, video games, anime (some of them), fanfiction, reading, fangirling, writing and pop culture references.
They quite often have a good sense of humour and are interesting, intellectual (when they want to be) people.
Often Geek Girls can fit into a group of 'normal' girls easily. Sometimes it may come as a suprise that they are geeks. But the term for geek has broadened and often, Geeks are simply regarded as the cool people who simply live life the way they want.
There are hardcore geek girls, but these may often blur into the socially awkward nerds.
Amanda Siefrieds character in Jennifers body is a prime example of a geek girl.
Geek Girl: "Ummmm ya no"
Geek girl: "Sorry i'm busy"
*At home on computer eating Nutella in pajamas*