I would start by doing a thorough clean out of all bedding - including sweeping out the dust if possible. Also clean off all the roosts and nest boxes. If you truly have an infestation, Sevin Dust is probably your best bet - you can find it in the gardening section of most box stores. Sprinkle it on all surfaces - roosts, nest boxes, floor - anywhere the birds sit - and then add fresh, clean bedding. You will also need to treat the birds themselves.
That said, I actually hate Sevin Dust with a passion because its use is one of the causes of the reduction of bee populations, so when it comes time to clean out the coop again, try to keep this layer of bedding from ending up on gardens, as it will kill your beneficial insects.
Many people use food-grade DE (Diatomaceous Earth) instead, as it is an organic product. I have used it with limited success and after spending hours researching it, including multiple scientific studies, I don't believe it works as well as many people swear it does. But I figure - if it works for you, its a better alternative than the Sevin Dust so I would never tell anyone not to use it.
Incidentally, before going through all this, you might want to verify that the birds actually do have parasites and the best way to do that is to go out after dark with a flashlight, as they are most active at night. Shine the flashlight on their skin, particularly around their vent and in their armpits, and if they have them, you will likely see them crawling around on the skin.
