I'm looking for a mod which lets you add any object to your inventory so you can carry it anywhere you go. Does such a mod exist?

AFAIK a mod like you describe does not exist. There are several issues that would make such a mod extraordinarily difficult or impossible. First, the majority of objects in Oblivion are static and have static havok (collision). The mod would have to convert the collision of thousands of objects from static to dynamic. Second, the mod would have to create icons for all of those objects so that you could see them in your inventory. 'Short answer: Don't hold your breath.

I can see it now, posters all over IC saying "will whoever picked up White Gold Tower please put it back!"