I would invest in several sets of OdorEaters shoe inserts -- the ones that have charcoal in them. Close up the fabric in a bag with the inserts for a couple of weeks; the charcoal should absorb the off-odors.
This worked for my featherweight case after trying *numerous* other tips such as dryer sheets, soap bars, sitting out in the sunlight for days, etc. Those shoe inserts took away every bit of the musty odor that was in the box.
You can try airing the pieces out for several days (in the shade so the fabrics don't fade). If you're still not satisfied, I would try the OdorEaters.