This word has several slang meanings. They are:
1) To engage in casual sex with someone.
2) To give someone a dirty look (In London at least).
3) To give someone a poor deal.
Because of this, a sentence like "he screwed me" can be somewhat ambiguous and so context is important.
1) She's such a slut, she screwed Billy the other night and Davey the night before.
2) So we broke up on Monday and then when he walked past me yesterday he screwed me and I just flipped out.
3) So I just wanted to buy those chocolate chip cookies because they are the best thing on this Earth but oh my godthat guy in the shop screwed me over so much, I mean since when did five little cookies in a packet cost so much? I swear they were one pound yesterday and now they're like four pounds, almost.