Hmmmmm, the toy thing I totally understand - DC's need toys and things at both houses so to keeps yours with you and his with him makes sense, and saves the children from having to cart things back and forth each time they change houses. I do this with my DC's and their Dad, but they are allowed to take smaller things like cars, barbies etc as they have tomns at both houses so it's no biggie if they get left behind for a couple of weeks.
The clothes thing is odd though, but it's not the first time I've heard of it - some parents seem to get a bit crazy when they separate. My step kids have this - if they take a single thing from ours to their Mums she will throw it in the bin. She has thrown away pants, bras, lipgloss, travel mugs, socks, a cardigan, a lego set......even party bags they have taken home with them. When challenged (by them) she says it's because she doesn't want her house to smell like ours 
This is also the reason she makes them get straight in the bath too. It doesn't bother me in the slightest but I feel sad for the kids. My stepson spent his pocket money on a cool lego kit recently and desperately wanted to take it home so he could take it to school for show and tell but he said he couldn't risk his Mum finding it and chucking it.
I have no explanation, other than she has a screw loose and from the clothes situation op I think your ex does too. Sadly, it seems really common that one (or both!) parents will behave like this. I don't get it at all - it only upsets the kids and makes the parent in question appear mentally unstable!
No advice really except don't rise to it - a reaction from you will make him think it gets to you, so he'll keep doing it.