Peter Gabriel era Genesis was pretty goofy, as well as some of his solo stuff.
King Gizzard and the Lizard Wizard is pretty much the goofiest band known to man right now; especially if you listen to their earlier stuff like Cellophane or Vegemite.
I second most of these other recommendations, but since I haven’t seen them said yet, The Magnetic Fields. Somehow manages to be funny while also being very geniune and touching, which I think is kind of what I look for in a band.
Captain Sensible. He was the guitarist for the punk band The Damned, but had a #1 hit in the UK with “Happy Talk”, a song from the 1949 musical South Pacific.
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