Mold spores are everywhere, but they require the right environment to grow. If your garage is dry, it should air out eventually, but it can take a really long time if the smell is strong. Increasing ventilation in the garage will help. If you can put a fan on it and crack open a window or door it would help.
I would try either baking soda or charcoal in containers in the drawers. There is another odor adsorber -- some kind of rocks or zeolite -- but I can't remember what it's called. I think the activated carbon works a little better than baking soda, but I'm not positive. You can find it in pet stores that sell fish -- they use it in aquarium filters. You can find it elsewhere but offhand I can't think of where. The only problem is that its "range" of effectiveness might not be very far from where you put it. If the cabinet will fit in a giant garbage bag, you could put activated charcoal in the bag with the cabinet and seal it up. I've treated books this way, but they're small and easy to fit in a bag.
I have also used the carbon from spent Brita filters to treat books. My theory was that the molecules in water (such as chlorine) that are adsorbed on the the carbon might be a different size than odor molecules, so the carbon might still have some open "pores". I emptied the carbon into a bag, put the book in the bag, sealed it up and forgot about it for a few months. It did work, and one advantage of the brita carbon is that it doesn't have the carbon dust that the pet store carbon has. But of course this is not practical for your cabinet as you would need a ton of used brita filters! I have also tried the bag method with baking soda, and it worked, but the baking soda got into all the pages and it's impossible to get it all out. It's annoying but I think it's actually good for the book because it neutralizes the acids in the paper and air, for a while anyway.