I regret that I haven't kept up with it the last decade or so but soon after it debuted in 1982, I became a big fan of Forbidden Broadway, an off-Broadway (and touring) franchise that parodies whatever's playing on The Great White Way at the moment, plus a few golden oldies. Every few years, they come out with a new edition but the truth is that the show is constantly changing in order to keep timely with what's playing in New York.
Its creator, Gerard Alessandrini, writes and directs and he used to actually perform in it. In the video clip below, he's the guy playing Tevye and Richard Burton. He's also very good at finding great performers who play in Forbidden Broadway for a few years, then go on to bigger/better things. The first song you'll see in there is sung by a young and hairy Jason Alexander. For a time, I hung around Forbidden Broadway a lot and became friendly with a lot of its players and even hired some when I was voice-directing cartoons.
We have here a half-hour-or-so of clips from the earlier days of the show. Some are from episodes of The Merv Griffin Show when he showcased the then-current production, and you'll see some songs repeated. For a while, a regular feature of every new version was some lady who was too old to play Annie dressed up as Annie, singing about how she was too old to play Annie.
There's no production of Forbidden Broadway running in New York at the moment, though someone may be doing the show somewhere near you. The shows being spoofed keep changing, the songs keep changing, the performers keep changing but this package of excerpts will still give you a good idea what it's like…