Lyrically, I think that Short People by Randy Newman deserves a mention in this thread. It went to #2(!) in 1977, only stopped from reaching #1 by that wonderful song *You Light Up My Life. *
Cone to think of it, the Beatles had a number of “weird” songs, but once again, I don’t know how high they charted. I’m thinking of “Rocky Racoon”, “I Am the Walrus”, and of course “Yellow Submarine”. There are probably more.
One of the weirdest (or most nauseating, depending on your tolerance for Aussie quaintness) has to be Rolf Harris’ Tie Me Kangaroo Down, Sport, which hit Billboard’s #3 in 1963, and featured the line “Tan me hide when I’m dead, Fred”.
Also, though it wasn’t Top Ten material, my vote for weirdest Top 20 single of all time is Eighteen With A Bullet by Pete Wingfield, sung in a loopy falsetto, and which peaked at (naturally) #18 on the charts:
*I’m eighteen with a bullet
Got my finger on the trigger, I’m gonna pull it
I’m picked to click now
I’m a son-of-a-gun
So hold it right there little girl, little girl
We’re gonna have big fun*
That’s the song I was going to mention, even though it only made it up to # 17. The weirdest song that hasn’t been mentioned yet has to be Elva Miller’s (known as “Mrs. Miller”) cover of Downtown. Picture a 60-ish woman who sounds like Ethel Merman on a bad day, accompanying herself on the zither. She only peaked at #82, but, hey, it was what some consider the Golden Age of Rock, so you gotta give her due props.
Sukiyaki. Actually titled I Look Up When I Walk, the name was changed to something Japanese-sounding that had nothing to do with the song for American release, a move Newsweek joked was equivalent of renaming Moon River “Beef Stew.”
Actualy, Horton sings this tune in Bob Clampett’s Looney Tune adaptation from the 1940s (one of the few times Warners actually licensed somebody else’s work, and surprisingly faithful while still having that typical Warner style.)
As well as the now-politically incorrect (and later removed) line, “Let me Abos go loose, Bruce.”
“Ben” by Michael Jackson (a love song for a homicidal rat)
"The Night the Lights Went Out in Georgia by Vicki Lawrence (even in the Deep South, people don’t get put on trial, sentenced to death and hanged the night they’re arrested)