There's a whole culture of mocking such units with invented ones.
My favourite so far would be "burger per square eagle", which is a unit of distance.
It's actually sort of a puzzle - you have to imagine how to interpret the units so that they match the result.
I remember starting off using someone's idea to take a bald eagle's average wingspan (2.7m - which is incorrect BTW). What follows is that the burger must represent volume - I modeled the burger as a half sphere with a diameter of 13cm, which yielded ~500ccm - sounded believable enough.
The only issue remaining was that the unit was very small - a small fraction of a millimetre.
Then again measuring things in megaburgers (per square eagle) sounds fairly natural - a lot like kilometres or kilograms.