When the strips were collected into book form, it included a flexi-disc with two of the Boingers' songs on it. "I'm a Boinger" was in fact written by Richard LaClaire and performed with Scott Freilich, Rich, Kazmierczak and Mike Bryydalski who collectively were known as The Harry Pitts Band. As far as I can tell, this was their only recorded song.
The b-side was "U-Stink-But-I-♥-U" by Bill Casler and performed with Chris Milnes, John Milnes, Danny Nastasi, and Scott Lepage. They formed the real life band Mucky Pup, and enjoyed a fair amount of success for ten years, releasing six studio albums. The band is still around (although with not entirely the original musicians) touring as recently as this past March.
Both songs were chosen from reader submissions as part of a contest. Mucky Pup went on to record a video for their song, and it continues to be one of the band's closing numbers. Although non-winning songwriters weren't contacted at the time, some of have since come forward to place their recordings online. I'm still partial to "I'm a Boinger" though.
A bird on the bass
A tongue, what a face!
At best, the music could be described as lame
Sure we look disgusting
But whose chops are we busting
In a year, maybe two, we'll seem tame
And three years down the track
We'll be a Las Vegas lounge act
We'll be back
We'll be back, 'cus we're the Boingers
Jimmy dropped his pants
And Ozzy dines on bats
And Hendrix played guitars with his teeth
The Deadheads got their Jerry
And Mom's got her Barry
And Ronnie listens to guys like Falwell and Meese
But if you don't know by now
Bill bit the head off a cow
That's no lie
That's no lie, 'cus we're the Boingers
Was Bowie ever a fairy?
Was Debbie ever Harry?
Was Elvis ever the King? let's not be reflective
Does Barbra wish she was a goy?
Is George really a boy?
Is Filthy ever Divine? - It's all subjective
Answers to all this
Lie with their psychoanalysts
I can't relax!
I can't relax, 'cus I'm a boinger!