I too nominate any and all novelty songs, like:
“Monster Mash,” which hit #1 in October of 1962 and then made back up to #10 ten years later in May of 1972.
“Itsy Bitsy Teenie Weenie Yellow Polka Dot Bikini,” which peaked at #1 in August of 1960.
“Come on-a My House,” which hit #1 sometime in 1951.
Thriller by Michael Jackson.
Lyrics, theme & a voice-over by Vincent Price. In a musical genre dominated by love songs.
The artist’s later problems only making things stranger.
“Tennessee Bird Walk” was another outta-left-field radio hit.
“…oh remember me, my darling, when spring is in the air
and the bald-headed birds are whispering everywhere
When you see them walkin’ southward in their dirty underwear
That’s the Tennessee Bird Walk (chirp chirp)…”
Two more ultra-weirdies from right around the same time as “Rock On”: Hocus Pocus by Focus, and Blue Swede’s version of Hooked on a Feeling (Hooga-chacka, hooga hooga!).
No mention of Muskrat Love yet? Now THAT is weird…
On WMOT, JAZZ 89, I just heard a Jazz version of the old Spiderman TV show theme.
Some info–
King Missile’s “Detachable Penis” was a brief enjoyable hit on mainstream radio in the '90s 
In fact, I’m humming it right now, and can’t get it out of my head…
Just out of curiosity, what do you find weird about this song? Is it because of the souped up disco version that Madonna did?
Before I post any nominations, one question:
Are these weird songs, or songs that are weird relative to the popular music trends of the era?
And then there’s Gary Puckett and the Union Gap’s “Young Girl.”
“My love for you is way outta line…”
My Name is Mud, by Primus. The bass is practically a drum, the guitar squeals, there’s a dialogue excerpt from “Deliverance,” and the lyrics are about a self-described “boring sonsabitch” - an unemployed, mentally unstable alcoholic who wears only navy blue clothing. And he’s telling us the tale of how he beat a friend to death with a baseball bat for informing him that his name is really Alowishus Devadandner Abercrombie, not Mud.
For me, it has to be YMCA by The Village People
It never ceases to amaze me when people celebrate, en mass, a wedding or even little Nathan’s Bar Mitzvah by dancing and singing to the glorification of anonymous gay sex at the mother of all boarding/bath houses:
*Young man - there’s a place you can go
I said - young man, when you’re short on your dough
You can stay there, and I’m sure you will find
Many ways to have a good time.
It’s fun to stay at the Y.M.C.A.
It’s fun to stay at the Y.M.C.A.
They have everything for young men to enjoy.
You can hang out with all the boys.*
I believe it made it to #2 but never #1, but definitely held a Top 40 spot for a while.
White Rabbit. Jefferson Airplane.
Good call on Gary Puckett- “Young Girl” makes “You’re Sixteen” look like “Ava Maria”.
Governor, my OP wasn’t clear, but what I originally had in mind were songs that didn’t sound like your usual top 40 hit- for example, if one of Zamfir’s pan flute epics made the top 40 (one did in the UK IIRC), or a cut from Lou Reed’s Metal Machine Music. Some have followed with nominations that are weird musically, others lyrically.
The strangest one that I can immediately think of is “Mmm mmm mmm mmm” by the Crash Test Dummies which peaked at #4 on the Billboard Hot 100 (cite). It’s certainly an usual ditty in the context of top 40 pop tunes.
That’ll Be The Day was on TV the other day. Great movie.
Another one I just thought of, “Mother’s Little Helper” by the Stones- an upbeat ditty about recreational pill popping, featuring sitar as the lead instrument- at least I think it’s a sitar.
Hands down, 1972’s “My Ding-a-Ling” by Chuck Berry, his only #1 hit in the US. Yes, the man who wrote and performed such rock classics as “Johnny B. Goode”, “Roll over, Beethoven”, “Rock and Roll Music”, and “School Day”, scored his only #1 with an audience sing-along novelty that relies on the double entendre “playing with your own ding-a-ling”.
Second place: Sister Janet Mead’s 1973 rock-n-roll version of the Lord’s Prayer. #4 in the US, 3 million copies sold worldwide. Religious questions aside, you’d have to admit that’s unusual.