I'm making a rhythm game and want to ask jam teams for music to use, especially music they made for their game in this jam. This could be considered to slightly influence votes, as stating what other game shares a given piece of music might direct players who like that music towards that game. Am I allowed to use such music? If so, can I state the game/team I got it from?

That's between you and whomever you ask. As long as you credit appropriately as defined by them.

Though I reckon it'll be rather difficult to sort something like this out, and that it'd be easier to just use existing free music.