At the risk of continuing to be whooshed, the preponderance of bass is the musical joke of the song. It gives the song (acoustically speaking) a “big bottom.”
I remember that from the animated film
“Rock & Rule”
Personal Favs
Patricia the Stripper - Chris de Burgh
My Ding a Ling - Chuck Berry
Shaddapa yo Face - Joe Doice
Chocolate Salty Balls - Isaac Hayes
If I had a Million Dollars - Bare Naked Ladies
Frog Kissing. This was a minor chart hit for Chet Atkins. While Ray may have recorded it, it was actually written by Buddy Kalb, who also wrote…
Lots of Uncle Bonsai songs would fit in this thread. They were a hyper-literate, satiric/folk trio with occasional Lehreresque lyrical touches. They pretty much covered the spectrum from very silly (Cheerleaders on Drugs) to very serious (Silent Night); somewhere in the middle were songs that could be funny and touching at the same time.
There are some samples here.
I’m 49 and this is the first time I’ve run into anyone else who had heard of the
Royal Guardsmen. 
Just about everything by the Bonzo Dog Band. Highlights include “The Intro and the Outro,” “The Equestrian Statue,” “Jazz, Delicious Hot, Disgusting Cold,” “Urban Spaceman,” “Beautiful Zelda,” “My Pink Half of the Drainpipe,” “Trouser Press,” “Look Out There’s a Monster Coming,” “Humanoid Boogie,” “Hunting Tigers Out in Indiah,” “Mr. Apollo,” “Tent” and many more. They were terrific musicians and songwriters.
I listened to My Ding-A-Ling with my mom. Talk about embarrassing.
If you like that one you will love The War of 1812. I like the Arrogant Worms, but think (musically speaking) that TDTiaB are better.
DaVinci’s Notebook is another group that’s musically tight but lyrically hysterical.
As a devoted Savoyard, I have long viewed this as a freakin’ masterpiece. It took me three or four tries to get through the whole thing, because I was laughing so hard.
I find most of Jonathan Coulton’s work fits fairly well into this category. The songs are smart, charming, and catchy – even if he never really does anything incredibly risky musically (they’re pretty derivative of their respective styles, but well-done nonetheless). You can stream all his music from his website. A couple of my favorites:
I’m Your Moon, a love song sung to Pluto by its moon Charon, as consolation for losing planetary status
I Feel Fantastic, about a culture of rampant self-medication gone awry
Space Doggity, this one’s actually pretty depressing – started out as a tribute to Space Oddity by David Bowie (for a songwriting competition – he won) and ended up being about the sad story of Laika, first dog in space (warning: if you’re a dog lover, you might just end up with dust in your eye, like me :p)
Well, if you think about it, back in the Fifties, there was a VERY fine line between novelty songs and rock songs.
I forget which critic I’m stealing this observation from, but… Chuck Berry may very well have throught of himself as a blues singer, and of “Maybelline” as a novelty song.
Was Gene Vincent’s “Be Bop a Lula” a serious rock song, or a novelty song?
What about the Coasters’ “Charlie Brown”- early rock classic, or novelty song?
Even things like Jerry Lee Lewis’ “Great Balls of Fire” and Little Richard’s "Tutti Frutti"come close to being novelty songs, really.
About the same age, and I actually have one of their 1960s albums buried somewhere with the rest of my LPs. As I recall, it has their Snoopy songs, as well as some of their originals.
That song was awesome. Do you know it got banned in South Africa for use of the term “bloody?”
If that counts as a novelty song, I’ll trump it with the Homer and Jethro version, The Battle of Camp Cucamonga.
The Battle of New Orleans was the first 45 I ever bought, so it makes me nostalgic. He also did Sink the Bismarck.
At 10 I was also quite fond of Monster Mash and Ahab the Arab. Pre-Beatles a lot of novelty songs charted.
However I’d be remiss not to add nearly anything by Tom Lehrer.
Pretty much everything by Richard Cheese (I like his version of “I Like Big Butts” better than the G&S version)
Alanis Morrissette’s cover of “My Humps” (which I actually quite like, despite an active hatred of the original version)
Dana Carvey’s “Chopping Broccoli”
Jonathan Coulton’s “Re: Your Brains”
Not sure they count as novelty songs, but several by C. W. McCall, including “Convoy,” “Round the World with the Rubber Duck,” and “Comin’ Back for More”
(the latter certainly does–it’s about cannibal Alferd Packer)
Rockabilly.
Oh, and ETA:
I just read Leiber & Stoller’s autobiography, and they describe writing it for the Coasters: They considered it more of a novelty, looking for something that would go well with the comedy style of the Coasters. But they considered them talented musicians who did funny songs, not comedians.
“Joy to the World”, the one with Jeremiah the bullfrog. Three Dog Night thought it too much of a novelty but needed one last track for Naturally so they recorded it anyway, then went on an overseas tour.
Unchained Melody by the Goons ( Peter Sellers and Spike Milligan)
I particularly like the middle part when each instrument seems to be playing in a different time signature.
Agreed. Shopvac and Re: your brains are also some good ones, though Shopvac is also pretty depressing.
Coulton’s stuff tends to be simultaneously upbeat, goofy, and depressing. Shop Vac, Skullcrusher Mountain, Betty & Me, The Big Boom…