Ionizers work by knocking positively charged suspended particles out of the air by canceling their charge--indoor air pollution almost always has a positive charge. They do their work very well--however, you do have to calculate a bit based on how large the room is, because if you leave a big ionizer going in a small room, you're going to wind up with negatively charged suspended particles in the air, and that's no better than the other way around. They also naturally create a thick, sort of sticky dust that collects around the emitters--the stuff that fell out of the air. This is what you wanted, but it can be messy to clean up, and you have to stay on top of it.
Me, I'd like to have an "Ionic Breeze" air purifier. Pricey, but should last practically forever, easy to clean, and extremely effective. There are some lower-cost knock-offs now, too.
If you want to get really serious about more than odors, you'll probably want an air sanitizer--a UV air sanitizer is designed to kill bacteria, mold spores, viruses, and other baddies...
You can get all-in-ones that combine ionization, a HEPA filter, and UV sterilization, too.
Something like that could make a big difference, particularly in a larger breeding facility. Fewer mold spores also means less chance of eggs molding in the incubators.