The phrase "strange obsession" refers to a very unusual or peculiar preoccupation or fixation that someone has with something or someone. Full definition
For the simple reason that I have a really strange obsession with sheet cakes. (wholeandheavenlyoven.com)
My boys literally cheer when I say it's taco night - although it might be because they have a very strange obsession with sour cream. (mostlyhomemademom.com)
And maybe check into your beloved's strange obsessions before tying the knot. (realtor.com)