You can store them in a trash bag so they don't get dusty over time. If you are a crafter, you can you buy wrap totes which are made to store wrapping paper. You could just use a cardboard box to store it. If you are crafty, you can create cardboard dividers, then put it inside another cardboard box to store the wraps one by one or by holiday.
I used to buy holiday wraps but I've gone cheap for the last 2 years...keke. I use brown paper bags from the grocery store. Typically when it starts hitting closer to the holidays, I'd save the paper bags and then gently cut and turn them inside-out....WAAH-LAAA...you get brown paper wraps.
I've always been a fan of brown paper wraps because then it leaves room for me to do all sorts of things with the decoration and personalized it as well.
/crafts