In the video for You Probably Get That A Lot, Linnell goes completely mute near the end, leaving the rest of the band to play on. He then comes back to say the "-ly" in the word "spontaneously."
That's also in the Album Raises Troubling Questions remix.
There was an anecdote about falling for a Snipe Hunt-like trick that John Linnell used to routinely tell between songs during a tour in 1999: While in Rhode Island, someone recommended he go out to a particular deli and try a local delicacy called baby fingers. The deli existed, but "baby fingers" did not - the punchline was a breathlessly exclaimed "...it was a trick, there's no such thing as baby fingers and the guy thought I was a freak!"
Another constant source of hilarity at the band's live shows: Whenever They play "Snowball In Hell," John and John tend to improvise a routine (or record one in advance) in which they mercilessly lampoon the sample that appeared on the studio bridge.
A running gag in the "Our Options Have Changed" tour was to have They Might Be Giants take calls to the Dial-A-Song service mid-show. The callers (played by Flansburgh) included Mama They Might Be Giants (who gave birth to quintuplets and, in the ensuing stupor, could only come up with three names) and an increasingly furious David Miscavidge, who speaks in a squeaky voice and sends the band all manner of baffling, empty threats.
"Did you say... what I think you just said — my hat looks good on me? I agree! I agree!" It makes an especially good Chew Out Fake Out because the song sort of dies down to create tension and then kicks back up again when it turns out the narrator is still happy. The music is being funny as well as the lyrics.
On the Amazon release of "Here Come The AB Cs," there is a re-recorded and re-worked version of their song "Hovering Sombrero" (originally of their "Mink Car" album). The original song is slow and relaxing. Their new version is fast, cacophonous, and only one original verse is kept. Every other lyric is replaced with Linnell, singing gibberish in a comically deep voice, and several overdubs of Flansburgh in the background shouting "B!" and "BO!" whenever the other John is silent.
Most of the in-between banter and discussion from the Frank O'Toole radio show on WFMU counts as this. It might be one of the silliest things ever recorded, and can be downloaded here
Special mention goes to the full version of "Doris Cunningham," as it was broadcast on the show. It's a clear example of the sort of humor that would later lead to such sketches as "Lesson No. 19" and "Turtle Songs of North America."
"We Just Go Nuts at Christmastime", the first song proper from the show, might be either this or a Tear Jerker:
Seems like only yesterday, our D-I-V-O-R-C-E, I love you both, but yuletide is still H-E-double-L for me
...but the spoken word on the bridge of this version qualifies it by a long shot:
Hi, this is John [Flansburgh] of They Might Be Giants, and you're listening to the Frank O'Toole radio show on WFMU. If you're driving your car now, we urge you to sit back, relax, close your eyes, and drive really fast.
"You're On Fire" is incredibly blasé, even though the narrator's telling the subject that their head is on fire.
As I'm sure you're aware You've got one of those rare Combustible heads I read an article all about them
The second verse is something to behold
No, you can't park there Whoa. Your head's on fire
From The Spine Surfs Alone, there's "Skullivan," a hilarious inversion of their usual take on Lyrical Dissonance. It feature's Flansburg's distorted voice wailing such lines as "I'll make you a pot of tea, how does everyone like their tea" and "I rented Tootsie, you gotta check this out" as Linnell chants the refrain over a tense, powerful instrumental.
The live version of "Hideaway Folk Family", as captured on the online-only release First Album Live, has them taking the Subliminal Seduction parody aspect of the "fake backwards" singing section a little further: Among the usual nonsense syllables are "Natas", "Yasmin Bleeth", and "Meryl Streep".
"Erase," off the 2015 Dial-A-Song reboot (and later, Glean), is a gleefully dark tune which includes such gems as:
Think of this as solving problems that should never have occurred Please don't call it strangulation, that is such an ugly word
"Thinking Machine", another Dial-A-Song track (later on Why?), is a duet wherein Flansburgh sings Word Salad Lyrics and Linnell responds pretty much as the listener would:
Flansburgh: Gurb long trom flom dim fim lim
Linnell: Pretty sure thatís gibberish
Flansburgh: Dog dog dog dog dog dog dog
Linnell: Now youíre just repeating the word "dog"
This particular passage is made funnier by the music video, where dogs materialize with every repetition of the word dog... Then one of the dogs promptly lifts its leg...
Off the same album: "Hello Mrs. Wheelyke," wherein Flansburgh's sincere, mundane calls pair with Linnell's spirited, absurd responses.
"I Made A Mess," whose completely dramatic delivery would be a textbook case of Felony Misdemeanor—except each passing verse suggests the eponymous Noodle Incident is far worse than the last verse implied.
I'll need a ton of mops and glue And soap and towels and paint And power tools
"Oh You Did" from Why?, where guest vocalist Robin Goldwasser portrays a parental figure in the verses and the Johns portray the child in the chorus: The trouble the kid gets into is increasingly specific and elaborate, from saying rude things about their dad and dropping eggs from 14th story windows to whatever actions led to the questions "How did the carton of milk get filled with shaved off puppy hairs? What's that river of water doing pouring down the stairs?". Meanwhile, the chorus takes the form of an apology from the child, but the second time it's delivered in a much more mumbled, insincere manner.
The video for All the Lazy Boyfriends shows various boyfriends getting 'sign-shamed'; the transgressions listed start with reasonable bouts of laziness like "I clip my toenails in bed" and "I never make reservations" but soon turn to absurd things like "I pay someone to shell my pistachios" and "I don't double-check my logarithmic functions". Also included are boyfriends that "(have) worked 15 days in the last 15 years" and "always use the warps". Even on some of the more normal ones, the visuals are still fairly ridiculous.