i haven't used vinegar to get rid of odors in fabric yet, but i have used baking soda with success. i was not 'gentle' with my ties, i threw them right into the wash and washed them like any other laundry. they held up just fine and made me believe they will hold up to any application i use them for. there is a really large amount of fabric in a tie !
i would thinks sunshine will help too,
good luck!