Official answer: a genre which I like to call "telephony" or "imaginary rock".
It's meant to represent an oddly specific music taste popular among certain people who grew up on the internet. These bands are usually melody focused like the Beatles, court an 80s aesthetic, write storytelling lyrics that are morbid but playful and are willing to experiment with electronic and acoustic sounds.
The shared fanbase existed long before this show, so "telephony" tries to be a descriptive category, not a prescriptive one. The older generation of fans tend to like They Might Be Giants, Lemon Demon, and Tally Hall (and sometimes also Sparks, Oingo Boingo, OK Go, or The Aquabats) while the newest generation has added Jack Stauber, Cosmo Sheldrake, Will Wood, Bill Wurtz and more to the mix.
But the bands listed above are just a jumping-off point. It's a nebulous label, as it should be. If you're wondering how close your favorite band is to my personal idea of the genre, though, I made a little diagnostic quiz you can try.
(More truthful answer: Whatever I like to listen to and think my friends would like too.)
When I started this show, some friends brainstormed name options which I put in a Twitter poll. "Telephony" won by a landslide, with "imaginary rock" in second.
"Telephony" is actually a word from telecommunications technology. According to Wikipedia: "the field of technology involving telecommunication services for electronic transmission of voice, fax, or data between distant parties."
The word suggests an internet fanbase or online radio show like this one. It's nonsense-sounding, like "fabloo", and doesn't describe the genre enough to pin it down. It feels silly and fun to say but means something important. I don't know, it's just a word. But it's a nice one.
Thanks to Felinium (for doing the show art), Bdluejay (for suggesting "telefunny"), OK Glass (for being a cool dude), and everyone in They Might Be Lemons for sculpting my entire music taste. This show is for you.