I'm not sure about papercraft, specifically; but, I've seen a lot of people at conventions transport a variety of model terrain using large plastic buckets or tubs (with lids). I think this would probably work well, as long as you avoid mixing large, heavy items with structures that are very light and fragile.
I would sort out the items according to size, weight, and sturdiness. If things don't fit in neatly, it might be helpful to have a little bit of padding material, like foam. Use a separate box or bucket for collections of smaller items, like the barrels there. I use a fishing tackle box for my Shadowrun minis. I've found that it's helpful to have an extra small box around to carry broken bits of things, if any parts fall off and I don't have any non-dried glue.
It would be tough to transport that whole diorama as one piece; it's much easier if you can remove the houses, and things, and package them separately.