If there are no obvious signs of mildew, I would just try to find a place to hang up the various pieces of fabric where they can air out for a time. Once upon a time we all had clotheslines outside in our backyards that were perfect for such!
Your other option is to wash it all. I would do it in warm water and a small amount of your regular laundry soap along with some baking soda added to help deodorize.