The show tosses you between absurdist family comedy and apocalypse mythology without warning, and somehow that violent tonal whiplash becomes the entire point. You're laughing at a cat girl stealing apples one scene, then learning the end of the world depends on whether these misfits can raise her right, and the show refuses to choose which version of itself it actually is. That refusal is what makes it work: a genuine found family wrapped in the kind of comedy that treats its own premise like a joke you're all in on together.
Midarezaki Ouka works for Japan's agency for supernatural phenomena and is used to strange events, but his life turns upside down after he catches a small cat girl stealing apples in a shopping district. About a thousand years ago, the destructive being Enka was defeated, and before dying it swore its child would wake and finish destroying the world. In 2063, DNA testing turns up several possible heirs, but no one can tell which is the real one. The agency's answer is Operation Peaceful Family: put the candidates together under one roof, watch them, and hope the true child grows too fond of its family to destroy the world. Ouka is made the father without being told first. The mother is Kyouka, ruler of a demon underworld and a candidate herself. The children are Teika the lion, Gekka the jellyfish, Yuuka the oni, Ginka the cross-dressing son of a mafia family, and Hyouka the bioweapon. The result is a sci-fi comedy about a very strange household.