As someone with a couple of allergies and many sensitivities, I can tell you that a lot of fabric stinks. Fortunately, most cottons can be cleaned. I'm a fan of prewashing anyway, part of that is to take away the scents and treatments applied to new cloth.
Fabreeze is perfect for this sort of thing, even without washing. I've found that when I have bought bags of scraps that turn out to be severely smoke infested, that just spritzing Fabreeze on both sides and letting it dry will help tremendously. If you wash after the spritz, it will take tobacco smoke out completely.
I still haven't found anything that completely removes moth ball odor. Maybe I'm just super sensitive to the odor, but I don't even try to salvage fabric with moth ball smell. I have a lovely shop near me that specializes in fancy fabrics and trims for saris and such, many of it is imported shipped with moth balls. I have to sniff test anything/everything in the shop before I buy.