freshening musty furniture?

i had planned to use some old family furniture that has been in storage (apparently rather damp storage). many pieces have a decidedly unpleasant smell--- not just a wee bit musty and 'granmother''s house', but sour and mildewy. most pieces look fine but some had small dots of pale fuzzy mildew on them.
aside from no budget to replace, these are sentimental pieces. is there a DIY way to clean them and lose this smell? thanks-