Spike Jones did “I saw Mommy Screwing Santa Claus”. The master apparently was destroyed by Spike Jr., but I’ve had credible sources claim they’ve heard it.
Angels Using Holes of Glory
um… can’t think of any more 
Rudolph the Big Gay Reindeer
Had a very shiny rear
Covered with globs of K-Y
Everyone knew he was queer
All of the other gay reindeer
Used to sing and write him poems
They couldn’t wait to mount Rudolph
And bury all their reindeer bones!
Then one drunken Christmas Eve
Santa came to play
“Rudolph with your ass so tight,
Can I please bang you tonight?”
All of the elves they joined in
(Though a few of them winced in pain)
They lined up in Santa’s workshop
And made a Merry Christmas daisy chain!
Bah, who needs Fenris when we’ve got Dire Wolf 
Gotta say, Dire Wolf, that was inspired!
I Saw Mommy Felching Santa Claus
The Little Hummer Boy
Hark! The Harlot Angels Sing
The First [time for] Noel
Good King Worcestershiresauce
I can’t vouch for Rudolf the Brown Nosed Reindeer, but I have a copy of “Randolph the Brown Nose Reindeer” (He was just as fast as Rudolf but he couldn’t stop as quick".) And a song about Santa getting a DWI.
Santa’s coming and he’s gonna KICK your ass,
he’s gonna kick your ass,
he’s gonna kick your ass…
Santa’s coming and he’s gonna kick your ass,
Cause you’ve always been a rotten little brat.
Reindeer coming and they’re gonna bite your wreath,
thery’re gonna chew your welcome mat,
swallow your kitty cat,
Reindeer coming and they’re gonna eat your begonias,
Cause Santa hasn’t fed them in a month.
Santa’s coming and he’s gonna KICK your ass,
he’s gonna kick your ass,
he’s gonna kick your ass…
Santa’s coming and he’s gonna kick your ass,
Cause he’s sick of shoveling snow and reindeer poo.
Elves are coming and they’re gonna steal your turkey,
Wreck your TV,
Burn down your Christmas tree,
Elves are coming and they’re gonna trash your home,
Cause they ain’t got nothing else to do.
Santa's loaded with attitude,
He's loud and drunk and smelly and rude.
His workshop's been closed by an auditor,
And Mrs. Claus ran off with her chiropractor.
Santa’s coming and he’s gonna KICK your ass,
he’s gonna kick your ass,
he’s gonna kick your ass…
Santa’s coming and he’s gonna kick your ass,
Cause he’s had a really crappy year!
[sub]oooooooooh, my bum hurts![/sub]
See also “Santa Got Arrested”, by the same group…
Now to clarify I did not make this up nor do I condone it’s message. Also forgive my spelling…
Riding through the Reich,
In a big Mercedes bin
shooting lots of kikes
making lots of friends
rat tat tat tat tat
mow them mothers down
Isn’t it great to have the Nazi’s back in town.
Wow that certainly is a poor taste christmas carol. I shall now beat myself with a bat.
Dire Wolf that’s wonderful!
But wrong! Wrong! Just plain wrong!! Shame!
… but still wonderful!
*C cups roasting near an open fire
Jack’s gal nipping at his hose
Girlfriend Carol being played like a lyre
Nekkid couples dressed in birthday clothes
Everybody knows a little snack and nibbled toes
Help to make the moment right
Tater tots with their eyes all aglow
Will help Mr. Potatohead come tonight
They know that climax is on it’s way
From using adult toys and pics of Doris Day
And every naughty little date is going to spy
To see if monkeys out a butt can really fly
And so I’m offering this simple wish
To adults that frequent the SDMB
Although it’s been said many times, many ways
Party naked, indeed.*
Hark the Hairlip Angels sing
fnrr fnrr fnrr fuh fnrr fnrr fnrrrrrr
HA!
You better watch out,
You better not cry,
You better be good, I’m telling you why,
Ashcroft’s cops are coming after you.
They’ll throw you in the jailhouse,
They’ll beat you with their sticks,
They’ll whack you till you’re black and blue,
Thats how they get their kicks.
You better watch out,
You better not cry,
You better be good, I’m telling you why,
Ashcroft’s cops are coming after you.
They watch you when you’re sleeping,
They listen when you’re awake,
They know every thought in your head,
And every move you make.
You better watch out,
You better not cry,
You better be good, I’m telling you why,
Ashcroft’s cops are coming after you.
They’ll lock you in the pokey,
They’ll keep you till you die,
They’ll say that they suspect you,
But they never will say why.
I will also vouch for “Rudolph the Brown-Nosed Reindeer,” as well as “Leroy, the Redneck Reindeer”.
But nothing beats “Weird Al” Yankovic’s Christmas At Ground Zero for sheer laughability, IMO.
You might hear some reindeer on your rooftop
Or Jack Frost 'side your windowsill.
But if someone’s climbing down the chimney
You better load your gun and shoot to kill.