In a same vein, “Blinded By The Light” or “For You” (Springsteen songs where Manfred Mann’s Earth Band covers were hits). Likewise for odd lyrics “Randy Scouse Git” by The Monkees.
How about songs that aren’t what everyone thinks they’re about? The best example of this that comes to mind is Extreme’s “More Than Words”, which gets played at weddings, and is not suitable for weddings unless you consider that an appropriate place to play a song that’s about a dude telling his girlfriend that she’s history if she doesn’t put out.
Or how about “I Will Always Love You”, which is about the singer LEAVING?
Or “Saving All My Love For You”, which is the mistress whining about how her boyfriend isn’t keeping his “promise” to break up his family to run off with her?
Or R.E.M.'s “The One I Love” - “a simple prop, to occupy my time”
I have to add this one - it was a very minor hit in the 70s, but hit the top ten in the 50s.
I’m not sure I consider that really weird, except that I would be willing to bet that the song is at least related to Cinderella’s Bibbidi-bobbidi-boo
Actually, someone did mention it. (Post 154.)
What? No love for Ray Stevens? How about the immortal hit Gitarzan!
Gilly, Gilly, Ossenfeffer, Katzenellen Bogen by the Sea
From Wikipedia, the free encyclopedia
“Gilly Gilly Ossenfeffer Katzenellen Bogen by the Sea” is a popular song written by Al Hoffman and Dick Manning and published in 1954.
The best-known version in the United States was recorded by The Four Lads with teenage girls Lillian Pasciolla and others on February 27, 1954. The best-known version in the United Kingdom by Max Bygraves, also recorded in 1954.
The recording by The Four Lads was released in the US by Columbia Records as catalog number 40236. It first reached the Billboard Best Seller chart on July 3, 1954, peaking at #18.[1]
El Watusi (1961) by Ray Barretto. I have no idea what he’s saying, but I have a very strong feeling that he wants me to do the Watusi. Now.
ETA: Oh, and Soul Finger. Because it’s about a Soul Finger.
I didn’t see a response in the posts following it, but I wanted to make sure this got recognized…
I see what you did there, CJJ*.
How about Cheech & Chong’s “Earache, My Eye”?
Just reread the lyrics and I’m not seeing what you’re seeing. Were that the case, then “Words of Love” by The Mamas & The Papas would be in the same vein.
I can’t believe no one has yet mentioned Star trekkin.
Bloody this was all over the radio in Aus in around 87, and was in the charts in both the UK and AUS.
I went to a pub one night and after the 12th time this got played on the video jukebox I was ready to glass someone.
What in the wide world of sports is a “a spring clean for the May queen.”?
“Glass someone”?
Did I miss the mention of Surfin’ Bird by the Trashmen?
Bram Tchaikovsky’s “Girl of my Dreams” briefly made the American Top 40 in the summer of 1979. It’s about an inflatable sex doll.
Most unexpected place where I heard it: on the overhead speakers while walking at the mall a couple years ago. 
Smash a glass into an opponents face
We did Kate Bush Wuthering Heights, which I like…
but Babooshka is way weird, and got to number 5 in the UK (and was a bigger hit in Aussie).
Speaking of Aus -> anything that charted by Rolf Harris is weird:
“Tie Me Kangaroo Down” (with the Beatles), “The Court Of King Caractacus”, “Two Little Boys”, “Jake The Peg”
Two of my favorite “kick-ass” songs of all time were really weird pop hits:
Janie’s Got a Gun - Aerosmith
Smooth Criminal - Michael Jackson
These songs both kick a lot of ass, but they are kind of bizarre songs when you think about the content vs the energy of the songs themselves. You’d normally expect a song about a girl killing her father or a young girl getting gunned down to be sad, somber, etc. But these songs are the exact opposite.
That being said, MacArthur Park is just one of the weirdest songs period. What drives a person to write such a passionate and otherwise beautiful song about a cake that gets destroyed in the rain? It’s surely a metaphor but what a weird one.
Did “Video Killed The Radio Star” make it?