The Diary of a Crazed Family (2008)

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Midarezaki Ouka is used to having strange things happen to him -after all, he is the head of the Great Japanese Empire Paranormal Phenomena Bureau of Measures. But when he catches a small cat girl in the shopping district stealing apples, his whole life rearranges to fit a new operation...

OPERATION COZY FAMILY.

Thousands of years ago, Enka the God of Destruction, was killed. However, with a dying breath it claimed that its child would appear and destroy humanity. Now in futuristic Japan, all of the potential children of Enka have been found and placed into a haphazard family.

Teika the lion, Gekka the jellyfish, Yuuka the oni, Ginka the cross-dressing mafia son, and Hyouka the bioweapon--along with their parents Ouka and Kyouka (the ruler of a demon underworld)--all live under one roof in a family frenzy.