What about hanging kitchen cupboards from the ceiling of the basement? You could probably pick up used ones on craigslist.org or in the newspaper. At least it will be up and away from the dampness. You could still fold the fabric but keep them in plastic bags so the damp smell cannot get to them. I would use wall or upper cabinets for this,passing up the lower or base cabinets. When you have a nice day, open the windows, open the bags and air everything out. There are Rubbermaid storage cabinets available but I don't have any experience with them. Also, a ceiling fan or a dehumidifier up on cement blocks may help. Good luck.