What I have done to create new space is to organize items by where they are needed. For my sheets I fold them and put one set into one of the matching pillow cases to keep it all together. I emptied a drawer in our dresser and keep our sheets and towels there.
I try to use every available space I have. Under beds, behind armoires, all in plastic bins or vacuum bags. In the bathroom you can buy a small hamper and keep supplies in it instead of using it for the dirty clothes.