First edit what you have so you're not organizing gift wrap you'll never use. Then choose one system that fits the available space: an under-bed organizer, an over-the-door organizer or, for a larger collection, a rolling gift-wrapping station that can be stored in a closet.
Keep everyday favorites within comfortable reach and move less-used pieces to secondary storage. Before buying an organizer, measure the usable space and check that you can still open drawers, doors and lids fully.
Store pieces by occasion and use, not simply wherever they happen to fit. Label the outside of each container with enough detail that next season you can find the right box without opening them all.
Mr. Organized's Answer