There’s a Bill and Ted musical, and here’s the hyperlink you need to click to see it.
This seems to be legal. Judging by an interview with the writer, this is a situation where the rights are contested by multiple parties. The creator seems okay with it, judging by his interview, and that’s good enough for me.
Also check out the interview with the man who played the rapping Grim Reaper. He gives the same sort of slightly-sarcastic answers that I would, but there’s some sincerity there as well.
As for the songs themselves, I’m quite fond of Sigmund Freud’s anthem Relax.