Short answer to your question: no, ozone generators don't kill musty odors permanently. One time use to remove contaminates, like smoke damage, sure. You don't want ozone in your house routinely. As others have noted, it is hard on your lungs, and terrible on rubber, not to mention colors. It is well studied, and you need to ignore the pro-ozone material out there that is mostly sponsored by the companies making ozone generators.
So, sorry that things smell musty. I hate that smell, which comes with lots of mold spores, but thanks a whole other ball of wax. If things smell musty, you have damp and mold. I think that the better solution is to dry things out, e.g. ventilate the basement/crawl space, seal the space up and dehumidify the air. There's a separate thread here on dehumidifiers, with a number of great suggestions.
Good luck!
All the best,
Peter