De-Stinking The Unwashable

Put in a ziplock bag and surround with good quality clay cat litter with baking soda. The smell should be gone in a few days, and the cat litter will help pull out any oily stains.

The baking soda/corn starch works wonders. I've used it myself for stuffed animals with mechanical innards. When storing them long term, my grand mother taught me to place charcoal brickets in corner of the boxes to absorb the musty odor.

Sunshine.....lots of out door sunshine......won't work where I live
Northern Indiana and we don't get much sun in the winter.....but maybe where you are it would work. I store things with a few dryer sheets for a fresh smell.

Not sure if this will work, but for musty books I've been told to store them with newspaper for awhile to absorb the smell.

Since I like the smell of old books, I've never tried it.

I'd wrap the ornaments in tissue paper, and store crumpled newspaper in the box with them, not touching them.

Also put an old knee high or cut off pantyhose over the end of the vacuum hose. That way if anything is loose it wont be sucked into the vacuum and possibly losted.

If you include a bag of Christmassy potpourri in the storage box with them this January, then they may smell a lot more pleasant next year.

don't store them in cardboard as the box itself will absorb moisture through the year and pass it on to the contents.

plastic storage crates, on the other hand, could seal up so tightly that moisture is trapped within. a top that doesn't fit too closely, or adding ventilation by drilling some holes in the container may help

add a desicant, you know, like the little packet that comes in the shoebox. google it to find an appropriate product/supplier near you. (seems desiccant is an acceptable alternative spelling based on my searches. I'm in the UK, so it may be a US/UK spelling issue!)