I have a folding craft table that I use in our guest room. Most of the time it's open (just one leaf - I don't have enough space to put them both up). But when we have company or need more space in there, it's easy to drop the leaf/leaves down and roll it out of the way. It also has a really deep, long drawer and a shelf underneath, so it's easy to store the basics away. Maybe you have another use for it, too, so it can pull double duty. When it's open, there's a ton of space underneath for your boxes if you can leave it up.
Venture Horizon Delano Folding Craft Table - Sewing Tables at Sewing Table Shop
Aside from that and a couple of DVD towers, I store everything else in half of the closet. I can't imagine not having any closets!!
The only other idea I can think of, besides Tracy's, is underbed storage. Or think 'up!' There are always those things we don't use too often, and for me they go as high as possible to keep out of the way and I just keep a stepstool handy.
I'll be interested in hearing more ideas!! Good luck to you and I hope you find a solution to your predicament.