In addition to the previous suggestions, there are a few seemingly non-scientific methods museums use to rid garments of smells.

Placing the garment in a closed box for a few days with a qualitity of cat-litter is one - the litter absorbes the odour.

Neat vodka sprayed lightly onto the affected area is another - the alcohol is supposed to reactivate the residue causing the odour, and the evaporation helps take it away. Vodka is colourless and near odourless, but pure alcohol is an option.

Dry cleaning is good, but that uses chemicals that lift dirt, but not always the cause of the odours, and can leave residue of their own.

A mild talcum powder (baby powder) can be sprinkled onto the garment and left for a period. The talc absorbes grease or oils and can be easily shaken and brushed off.

One of the best methods is steam and sunlight. A thorough steaming from a proper garment steamer (or over a kettle spout) to swell and loosen the fibres, and then hanging in open sunlight with a mild breeze usually works well. The steam needs to properly penetrate the fibres - if held horizontally over the steam, it will pass through the cloth.

The good thing about both the alcohol and the steam is that they sterilize the garment at the same time, so maybe a combination of the methods would help you.

These are all good for body odours, but the wool of the kilt may be the cause, and is natural. Dyes can affect the smell, and natural oils in the wool often 'mature' over time, and these can often seem fusty or musty (like a dirty, damp dog after an autumn walk in the woods) and are a characteristic of vintage tweeds. But again, the steam and sunlight trick will usually do for these, too.

Hanging in fresh air, such as under the eaves of a porch, for a few days could be all you need to do - but storing in a hanging wardrobe rather then folded in a drawer is always better.

Let us know how you get on, and what success you have.

Good luck..!