Nodoka is a fucking sociopath. She's the one character in all of LiL that if she was written out of the story I wouldn't miss her at all.
Not contesting the first point, but the second I can't agree with. The story is 100% better with her in it:
1. She gives Yumi a reason to trust Sensei after the unfortunate bridge incident
2. She's even more of a catalyst to Rin's not-so-homie-like attraction to Sensei
3. She's an excellent source of external conflict directed at other girls, so it's not Sensei always filling that role.
If she was a one-dimensional D&D villain whose sociopathy always manifested slasher-film style, I'd agree. But she's a deep and complex character, so brilliant she has little in common with the peers she cannot empathize with. She reminds me a lot of Mia from Californication, only less self-centered. Nodoka is ruled by her desire to experience everything, to better be able to write about it. She may be a sociopath, but without the borderline or disassociative disorders to really turn her into a monster. Instead, she's this giant gray area of amorality that makes her interesting as fuck, if you can get past the way her manic episodes are written.
Edit: Not to mention, Hot/Crazy axis in effect.