I've heard "say again" but wouldn't say it myself. I don't think I've heard "say it again" and also wouldn't say it, even though it is grammatically correct. It would sound abrupt, unnatural and rude. It also sounds non-native (because of the "it"). Could you say that again, please? Sorry, I didn't hear you. Could you please repeat that? Less polite and not advised (but fairly common in the real world) What? Huh?

There's no difference, but "say again" isn't correct English. It might sound okay if you say "say again?" with a rising tone, as a question, because this sounds a bit like the idiomatic (but slightly dated) phrase "Come again?" (which means, "I'm sorry, I didn't hear you, could you repeat that?"). I don't know that I've ever heard anyone use "say again?" in place of "come again?", but some people might use the phrase this way. If I did hear someone say it, I wouldn't think it sounded too strange, as long as it was spoken as a question.