I used to be in a band which did a lot of comedy songs, but it was back in the 1970s, and most of them don't seem that funny any more (mostly ribald old folk songs)... But we did once support the man I consider the funniest singer I've ever seen. The room was in stitches through his whole set. Again, some of the humour might not have worn well, but these are my favourites of his:
https://www.youtube.com/watch?v=6p8cIjqBFls
https://www.youtube.com/watch?v=XQm_8uoljWM
Another good source is Tom Lehrer:
https://www.youtube.com/watch?v=I9C2v1oLXQo