Removing Musty Odors from Old Books

This is a great question and there are a few ways you can go about it.

One option is to get some MicroChamber paper from Conservation Resources. This paper absorbs odors and traps them within the paper. By interleaving your books every 30 pages or so as well as inside each cover. Leave the MicroChampber paper in place for about a month and then change out and put new paper in as before but in different places, always keeping new MicroChamber paper at the covers. Keep changing out paper until the odor has diminished. This may not be the cheapest option, but it is the one that I have found to be the most effective. 

Another option is to get a plastic bin and some of the closet deodorizers. Put the books in standing up and fanned out with lots of space around them (you may need multiple bins and deodorizers) and add the deodorizer so it isn't touching. Leave them in the bin a month and then check on the progress. Replace the deodorizers as needed. This is a much slower process (six months to a year depending on how bad the odor is).

Finally, the least expensive option is to do as above with the bins but use bowls of baking soda in place of the deodorizer. Don't sprinkle the soda over the books as this will just create another problem. Again, this will be a lengthier process but if you have time, it will be the least costly.

I hope this give you enough information to decide what is best for you.