Any educated guesses as to the origins of this popular parody Christmas song?
I don’t know the origins, but I do know it pre-dates The Simpsons, in case anyone was going to give that answer. I remember singing it when I was in elementary school, back in the late 70’s.
We also sang a version that would go:
Jingle Bells, (so and so) smells
fifteen miles away!
He blows his nose in Cheerios
and eats them every day, hey!
It’s a piece of what Folklorists call, “the subversive folklore of children”.
Unlikely to be traced.
I believe it originated in reaction to the '60s Batman TV series. I never heard it before the TV show took off, but it was certainly popular during the show’s run.
In that case, I take full credit, and demand that you start sending royalty checks retroactively to 1977. 
I can confirm that it is at least that old. There was also a set of Batman jokes around that time, including a book that got passed around at school.
Q: Where does Robin go when he needs to go?
A: The Batroom.
Jokes of that calibre.
But the version of the song I learned was
*
Jingle Bells
Battman Smells
Robin laid an egg
The Batnobile
It lost a wheel
And the Joker got away
*
Followed by:
Q: What does he do in there?
A: (to the tune of the “Batman” theme): Doo-doo, doo-doo, doo-doo, doo-doo…
Ha! We’re the SDMB! We can do anything!
(FYI - we sang Voyager’s version in schoolyards in Erie, PA, circa 1980.)
I learned Voyager’s version somewhere around 1971. The funny thing is that I didn’t see the TV show until 1974 or 1975 in afterschool repeats.
That’s the version I learned, but my parents (Class of 1977, southern NJ) insist that the last line is supposed to be “And the comissioner’s eating hay” (Implying he’s an ass or something, I imagine).
That’s the version that was current in the late 1960’s when I was in grade school,
too - during the campy Adam West TV show’s first run.
The funniest appearance of the song that I can remember is during a Christmastime episode of the Batman animated series on the WB network. Joker sings the song as he’s escaping from prison or something, and merrily says, “I *love *that song!” at the end - followed by a pissed-off Batman muttering angrily, “I *hate *that song…”
It is a piece of urban folklore, like the coyote boffing the road runner and saying “beep beep this” or some such.
It was in the archives at the university where I studied in various forms in the mid to late 70’s–you know, when you had to troll through folders of collected junk to find anything, in what was laughingly called catalogued order.
I probably have a book somewhere with a number of folklore just like that – in fact it may be in the book “The subversive folklore of children” which I believe I had a class in.
It was the 70’s, I studied a lot of things, I was sort of all over the map for some ADD kindof reasons I’m sure.
I remember it as “And Commisioner broke his leg.” I was never very clear on that last line. I like “The Joker got away” better.
In the 1950s the elementary school kids sang
Jingle Bells, shotgun shells,
Rabbits all the way.
Oh, what fun it is to ride
In a worn out Chevrolet.
If we’re wide open, already:
Jingle Bells, Shotgun Shells
BBs in the Air
Take a shot at Santa Claus
And listen to his swear.
Always appealed to the iconoclast in me.
I remember this from around 1966:
Q: What did they call Batman and Robin after they got run over by a steamroller?
A: Flatman and Ribbon
Is it time to mention:
“I’m Popeye the sailorman
I live in a garbage can
I eat up the worms
and spit out the germs
I’m Popeye the sailorman…”
Well, it ryhmes with “egg”. I learned the same version in suburban Montreal circa 1976 and didn’t hear the “Joker” variant until the Simpsons.
The Greaseman once had a segment on his radio show called Fudgeman and Throbin. Um, never mind… :o
During my (mid-1970s) elementary school years, we adorable li’l tykes sang a few verses like:
(to the tune of "Batman:)
Na-na, na-na, na-na, na-na
Batman!
Swingin’ on a rubber band,
Down came Superman,
Popped him in the garbage can,
Batman!
(At the time we sang it, we didn’t quite get the innuendo - “rubber band” meaning condom, “garbage can” meaning “rear end”, or so it was explained to me when I was a much more sophisticated sixth-grader!)
My brothers & I also sang,
Jesus Christ,
Suuuuuperstar,
Who the hell
Do you think you are?
(or at least until my very Catholic mother heard my brother sing it, and we all got grounded for a week – just for laughing at the line!)