I'm not fluent in Fanfiction Speak, but I know enough to get by. I'm pretty sure OOC means that the characters behave Out of Character. OC means Original Character--a completely new, original character is introduced into the Twilight Verse, usually as a protagonist. AH means All-Human, meaning there aren't vampires in this version of the story, and AU means Alternate Universe -- most AH work is alternate universe, as are stories in which Bella's an orphan, or Emmett and Bella end up being the main couple, etc.
Some of us really just want Twilight-specific stories... like something that's an exact retelling of New Moon, and the only original parts would be Edward's pov and scenes he experiences that Bella didn't. Others really like pushing the envelope for "Twilight related." It's fascinating to see how some writers can keep the kernal of the characters (maybe their archetypes, or even their souls) while setting the whole thing during Prohibition or in a New York boarding school.
Oh--and to stay on topic, I'm recommending this as-yet unfinished piece of fanfic, "What Are You Doing the Rest of Your Life," by Kristen Elizabeth: http://www.fanfiction.net/s/4717739/1/W ... Your_Lifer
It's mainly an Alice/Jasper story--no Bella, but only because it's in the 1950s; it's still true to the Twilight canon. It starts not long after they've moved in with the Cullens; while Alice is attending high school with the others and flourishing with having a family, Jasper's still not comfortable enough with his self-control to venture out among humans. In the meantime, Someone Bad has come to town to stalk them--but who?
The author does a great job of catching the 1950's feel; her world feels really true, and the Cullens are definitely IN character. Also, she ends each chapter with a link to a picture of something referenced in the story... Rosalie's roadster or the Cullens' house. Pretty cool.