My list includes:
Tom Lehrer, Christmas Time Is Here, By Golly
Al Yankovic, Christmas at Ground Zero
Elmo and Patty, Grandma Got Run Over By a Reindeer
I’m sure y’all will remind me of others. 
Christmas at K-Mart Root Boy Slim and the Sex Change Band
Santa Doesn’t Cop Out on Dope Martin Mull
“Christmas in Prison” by John Prine
Keith
Ray Stevens Bad Little Boy definitely tops my list.
The barking dog “Jingle Bells”.
a fairytale of new york - the pogues. i haven’t really decided if this song is supposed to be funny or not, but i find the humor in it because i can relate to it. i don’t know about everyone else, but christmas for me is never like a very special episode of a sitcom. anytime you can call someone an old slut on junk in a christmas song, you win points in my book. the song is also sad, as the couple looks back on promises made and dreams they had in comparison to reality. i guess the song isn’t as humourous as it is true.
Merry Christmas From The Family by Robert Earl Kean.
Santa Claus and His Old Lady by Cheech and Chong.
It just isn’t a complete Christmas if I don’t hear this tune at least once.
I like ‘The twelve days of Christmas’ by Bob and Doug. I can really relate to their Canadian humour.
peace,
JB
Chipmunks Roasting on an Open Fire is my new favourite. My daughters like the “There’s something in the chimney” song.
Sick, sick family. Even the dog is weird…
I tend to like most “The Chipmunk Song” by you-know-who.
Whoops! Just posted some of this in the “favorite/least” thread. Oh, well.
Apologies for never remembering artists, btw. And it’s a little hard to hum a few bars this way, y’know? Anyway…
The Walking around in women’s underwear parody of Winter wonderland. This thing SLAYS me every time I hear it. It’s just so smoothly, suavely, sneakily perfect and I hate the original carol anyway.
The Bob and Doug 12 Days parody is a hoot, and so is the version with the wailing child, man battling the Christmas lights, wife hating her MIL, etc. For some reason I always lose it with the Christmas card guy: “I don’t even KNOW these people!”
Veb
I’m particularly fond of several tracks on the Twisted Christmas album, particularly “Holy S**t, It’s Christmas”, “Chipmunks Roasting on an Open Fire” and “There’s Something in the Chimney”.
“Weird Al” Yankovic’s “Christmas at Ground Zero” is also a nifty one.
I’m trying to put together a CD-R of my wacky faves, to send to friends as a gag so…
[hijack] I want to use a picture I’ve seen in a few places for the cover art–it’s of a nekkid Santa (except for boots and cap) lounging in a classic cheesecake pose on a fur rug. It’s totally wrong and I must have it. Anyone know where I might come across it? [/hijack]
Never mind–I found it.
“Apocalypso (Wiping the Smile Off Santa’s Face)” by Mental As Anything.
RichLather, that pic always gives me chills - it looks so much like a guy I work with.
Another vote for ‘Christmas in Prison’ by John Prine, which is both humorous and touching.
“It was Christmas in prison,
And the food was real good -
We had turkey and pistols,
Carved out of wood…”
“Let’s Have a Patrick Swayze Christmas” by Crow T. Robot.
Unfortunately, the lyrics are written out in dialogue form.
Christmas in Prison, by John Prine, yes!
Humorous? Sort of. Touching? For sure.
I’d have described it as wryly bittersweet.
Oh, and Merry Christmas From The Family by Robert Earl Kean is, indeed, bloody hilarious!
I like the Dredel Dredel Dredel song from South Park, even though it’s not really for Christmas. I also truly believe that the only way to sing Oh Little Town of Bethleham is to the tune of The House of the Rising Sun.