Here are the answers, complete with YouTube videos for all of the songs. Some of these are fairly obscure, and I had no idea that I'd find videos for all of them. I'm amazed.
rmd and essaying did the best. I can tell who the showtunes people are.
1. A Kiss is a Terrible Thing to Waste. From the musical Whistle Down the Wind, covered brilliantly by Meatloaf.
2. Drowse. Queen.
3. I Got Life. From the musical Hair.
4. 8th Wonder. Sugarhill Gang. The B-side of Rappers' Delight. (I am bloody shocked that I found a video of this!)
5. I Know Him So Well. From the musical Chess. (Holy crap. Whitney Houston covered this! Shoot me now.)
6. Paradise Garage. Tim Curry.
7. One In a While. Rocky Horror Show.
8. Wicked Little Town Reprise. From the musical Hedwig and the Angry Inch.
9. Heaven Can Wait. Meatloaf.
10. Afternoon Delight. Starland Vocal Band.
11. Take This Job and Shove It. Covered many times, Johnny Paycheck is the best-known performance.
12. My Melancholy Blues. One of my favorite Queen songs.
13. Tainted Love. Soft Cell, and lots of covers.
14. Forever Young. Alphaville.
15. Heroes and Villains. Beach Boys.
16. Cabaret. From the musical Cabaret.
17. The Golden Boy. Freddie Mercury and Montserrat Caballe.
18. The Mighty Stephen Hawking. MC Hawking.
19. Rock Lobster. B-52s.
20. A Little Priest. From the musical Sweeney Todd.