Can you post some photos of your rescues?
I agree with Kathy, it sounds like Flystrike.
You mention that the birds are in rough shape, had poop on them as well as lice/mites?
How are you treating this?
If they still have a lot of poop on them, it would be best to give them a bath. Get a tube of soapy water (Original Dawn works well) and give them a soaking and work the poop out of the feathers. If poop is encrusted, you may need to trim it out.
Wet feathers allow you to see the skin easily - check them over well for any wounds, cuts or places that may be infested with maggots. The bath may help drown some of the lice/mites, but once the birds are dry, give them a treatment with a permethrin based poultry dust or spray. It wouldn't hurt to treat the housing they are in too. Repeat treatment in 7-10days or follow the manufactures label.
Since they are in rough shape. Offer them some extra vitamins and a "high" protein feed like Chick Starter or an all flock type feed.
Just my thoughts