“2001 Sprach Kazoostra” – Temple City Kazoo Orchestra (1978) Although their cover of “Whole Lotta Love” (at the 7:29 mark) comes close.
“Shopping For Clothes” – The Coasters (1960) You could create an entire playlist of silly Coasters tunes but this one is my favorite.
Another of my all time favorite silly ones -- The Edsels' Rama Lama Ding Dong. The vid post lists this as from 1961 -- and it was a hit as a re-release in that year -- but it was actually recorded and released first in 1958 and was a regional hit in the South and a couple of spot in the midwest as I recall:
“The Big Rock Candy Mountain” – Harry McClintock (1928) The hobo’s fantasy. And from perhaps my favorite movie of all-time.
They were best known for their surf and car songs during '63 ~ '65, but Jan & Dean had a national top ten hit in 1959 with this bizarre bit of doo-wop:
“California Kid” – The Beat Farmers (1985) The entire story seems implausible. But funny! I ordered up a whiskey He asked me for my bread I paid him two bits And then I pumped him full of lead
Is "Tie Me Kangaroo Down Sport" silly? Perhaps not,but I think that "The Court Of King Caractacus" probably is. Both by Rolf Harris
Pre-surf Jan & Dean again with their 1960 tune about dirty tennis sneakers: Adding to the goofiness -- wow...the outfits. V-neck sweaters, bermuda shorts, knee socks and white slip ons. Just, wow.
Marc Parenteau of WBCN played this one to death back in the day. The humor is more dark than silly. You’ve been forewarned.
I haven’t found a recording to post, but a comedy group named Slap Happy did a dead-on parody of Ode to Billy Joe, as Ode to Billy Joel. Link to the lyrics and a 45 second sample are below. Ode To Billy Joel by Slap Happy