Learned about this site last week.
The Funny Music Project. Parodies, etc. You can listen to full songs from a bunch of artists. Music is available for purchase/download, and it’s licensed Creative Commons so if you find something inspiring you can use it and the RIAA won’t break down your door.
Also:
http://www.jonathancoulton.com/store/downloads/
Be sure to listen to “Re Your Brains”, it’s pretty darn funny.
You’re welcome.
If we’re going at the funny tour, I have some songs for you too:
All work of Tenecious D
Legend of Zelda Theme by System of a Down
I wanna fuck a dog in the ass by blink 182
I like dirt by the Thunderlords
You are a pirate by Lazytown
No feelings by the Sex Pistols (Johnny Rotten sings about how much he loves himself)
I, for one, do not want to fuck a dog in the ass. But maybe the head.
Just look up Tom Lehrer for some classic hilarious songs 
“Poisoning Pigeons In The Park”
Yup. Tom Lehrer was a genius.
Does he write the songs himself too? I mean, the melodies?
IIRC yes. The songs I recall of his work were all original. He wasn’t a parody artist as much as a novelty artist.
My son’s a big Wierd Al fan, we saw him in concert last summer in Baltimore. Good show, Yankovic’s about my age but still moves really well. He got his career launch from Dr Demento…