Are people using “1-hit wonder” and “novelty song” interchangebly?
Tequila Makes Her Clothes Fall Off - Joe Nichols, 2005.
I’d think they were if not for the inclusion of Barenaked Ladies, They Might Be Giants, and The Offspring.
For something really modern, there’s the entire output of Bo Burnham. My current favorite is “Oh Bo”.
Another that came to mind, Wally Pleasant. See “Stupid Day Job”.
Surely Jonathan Coulton qualifies? Plenty of his songs are done for comedic effect, such as “Re: Your Brains”.
She’s talking again by Henry Philips
100 Things Every Man Should Know by Tim Wilson
Dear Santa by Sean Morey
Don’t Look Now by Rodney Carrington
And a personal favorite:
Internet Porn by Da Vinci’s Notebook
I took that song completely at face value. I had no idea it was a ‘novelty song’ until I started going to some white clubs and seeing white people going all bananas about it.
I had already been a fan of Sir Mixalot, though, before Baby Got Back
Corky and the Juice Pigs - I’m The Only Gay Eskimo
Anything by Stephen Lynch - If I Were Gay, for example.
No argument from me. But both “If I Had A Million Dollars” and “One Week” are pretty representative of the Barenaked Ladies oeuvre. And “Pretty Fly For A White Guy” wasn’t a novelty either, it was a single song from a concept album that focused on the lives of people not living the American Dream. In this case, the poser.
Oh, surprised I’m the first to think of Jonathan Coulton’s “Code Monkey”.
…but not a real green dress, that’s cruel?
Okay, well, I only heard it that one time. I didn’t know they were serious. 
Grandma Got Run Over by a Reindeer? I’m not sure who does that. It probably doesn’t count, but my first thought was Eric Cartman’s verision of Come Sail Away.
ETA: I’m not sure Grandma was after 1984, actually.
I looked it up and it was definitely pre-1984. So just pretend I never posted. 
Throw in some Mojo Nixon like “Elvis is Everywhere”
Pac Man Fever? by… the guy who did Pac Man Fever?
Billy Crystal’s You Look Mahvelous and Rodney Dangerfield’s No Respect?
Dennis Leary’s Asshole
There was some song in the 80’s about Vietnam is was a terrible bunch of samples and “rapping” over music I forget the name now
The Rapping Duke… i forget who did this one also
Buckner & Garcia, but it was 1982.
“19” by Paul Hardcastle. That’s not a novelty song, just a one-hit wonder.
Bill Engvall and Travis Tritt collaborated on a song based on Engvall’s trademark comedy routine, “Here’s Your Sign”.
“Istanbul” was originally recorded in the 1950s, and was a big hit at the time.
That song is from 1981, and even says so early on.
Who would think it would still get played more than 30 years later, long after the singer’s death?