I would not put the wrapped cheese in a box - I think that would retain too much moisture. I have not noticed any migration of flavors or smells once the cheese is wrapped. Stacking ... I try to avoid it, on the assumption that it will prevent or at least hinder the gas exchange for which the cheese wrap is designed. I do often set one down, then put the next one with an edge on the first one, and the next one with an edge on that, and so on. If I can make the characters work, it looks something like this:
_\ \
Well, that doesn't really look much like it -- the slashes are too vertical. Hopefully you get the idea anyway. Every day or so I flip and rearrange so a different cheese is the one sitting flat.