The stupid fake-Italian accent song “Shaddap You Face” was a big hit outside of the U.S.
Another one: Convention 72 by the Delegates, in reality a radio DJ.
It’s one of those songs where it’s a question-and-answer format, where the interviewer asks questions, and the answers are snippets of popular songs.
It reached number 8!
For a long time, I thought I had just hallucinated that one.
That reminded me of a similar song, “Mr. Jaws,” which came out on the heels of the movie Jaws in 1975, and was a top-10 hit.
The 1970s were weird, man. 
lol you guys know DR demento is alive and well and doing a webcast show right ?
Oh, certainly, and not everything in this thread is a novelty song – though it’s interesting to note novelty songs that actually became big hits.
A lot of the other songs in this thread are just, well, unusual, by pop music standards, and surprising hits.
The Legendary Stardust Cowboy made it into the Billboard Hot 200 with “Paralyzed”. It was popular enough to be used by NASA as a wake-up song. The astronauts were so traumatized they made a record number of errors performing their duties that day. To this day it is the only song to ever be officially banned by NASA.
It was a big hit IN the U.S., too. I definitely remember it, because it was popular around the time I graduated from high school.
This professor of classical and sacred music does commentaries on progressive and heavy metal songs, and this is an excellent one, although I’ll warn anyone who might be triggered that he takes a few hits off a bong during the video.
He recently did one, with his wife, on side 1 of Boston’s debut album (something else that ended up being WAY more popular than anyone could have imagined) and incredibly, he did not recognize “Foreplay/Long Time.”
Back to the unlikely or unusual songs, don’t forget “Afternoon Delight”, “Havin’ My Baby”, “Disco Duck”, “Everyone’s Free To Wear Sunscreen”, and any number of other novelty tunes that have hit the charts over the decades.
If this has anything to do with Kate Bush having a #1 song 37 years after it was first released, yeah, that too.
This sentence makes me smile.
I had a boyhood friend whose father enjoyed wacky records. In addition to the Dolce effort was another song, don’t know by who, that went something like:
When you visit American city
You will find it very pretty
Just one thing you must beware
Don’t drink the water
And don’t breathe the air!
(Of course this was when the river in Buffalo still kept catching fire, and Lake Erie was much less clean.)
Tom Lehrer, Pollution.
Lehrer is great. Try Poisoning Pigeons in the Park or National Brotherhood Week.
Spoken word “songs” are dreadful to the extreme. “An Open Letter to my Teenage Son” by Victor Lundberg is one of the most egregious. It sold a million copies and went to #10 on the Billboard Hot 100 in 1967. It’s the worst kind of right-wing extremist diatribe, with the Battle Hymn of the Republic played as a background.
One critic said, “The track is essentially a rambling rant…about long hair, beards, glue-sniffing, whether God is dead, and George Washington.”
To end it all, the “father” tells his “son” that if he burns his draft card, he may as well burn his birth certificate, because he will no longer have a son.
Dreadful it is. It’s on YouTube. Listen at your own peril.
No Matter What Shape (Your Stomach’s In)
Began life (in my consciousness) as an Alka-Seltzer commercial. Made it to #3 on the Billboard Hot 100.
Another commercial (for Maxwell House coffee) also hit it big on the airwaves, IIRC (The Percolator Song).
I know that the OP asked for individual songs. But I’ve always thought that the degree of Nirvana’s popularity was astonishing. Since I like defeatist, depressing music, Nirvana is my favorite rock band since the Beatles. But it amazed me that so many others (mostly seemingly well-adjusted young people) liked them. Cobain himself seemed similarly puzzled, as expressed in “Bloom”.
Oh, and to the OP: “Seasons in the Sun”.
And even thought it wasn’t exactly a blockbuster hit, an honorable mention for “Gloomy Sunday”.
I just got back from some errands and was surprised to hear a disco cover of McArthur Park by Donna Summer on the radio. Naturally, it’s pretty bad. https://www.youtube.com/watch?v=H4ZaUoTRydU
Oh, lawdy, I remember that one when it was on the radio all the time in '78. 
Oh lordy. I remember when it was new. “Old men playing …Chinese checkers by the trees”? WTF, Was that change necessary?
Probably after Nixon’s detente and visit to China. /pulledoutofmyass
There was also one about the Jessica Lange “King Kong” movie which just as horrendous.