IMO, for lice/mites you will want a dusting of something like sevin dust. And, depending on which you actually have, you'll want to treat the coop, too. Lice pretty much live their entire cycle on the bird... they lay their eggs at the base of feathers, and don't nest in the coop. Most mites will actually nest in the coop, in small cracks and crevices...in bedding, etc. This is where they breed/hatch, but swarm at night usually, when the birds roost. The greatest numbers of them on the bird will be during the night, but there are usually some that can be found around the clock.
Depending on what you're dealing with exactly, they may be biting bugs, or they actually may feed on the dander or feathers, but not actually bite the bird. This is where a lot of those meds fail when used to treat lice or mites... they have to actively feed off the bird, while the meds are in high enough concentrations in the blood, to be killed. There's not even a chance of that if they aren't biters...
A thorough dusting of sevin dust, all up under the feathers everywhere... to include a dusting of the coop, roosts, bedding (if unable to clean it out and lay down a dusting before putting more back in) and nest boxs... will kill them no matter what kind they are, biting or not, lice or mites. You DO have to retreat in about 7-10 days... at least once... to get any that may be hatching. If you have lice, with eggs/nits on the feather shafts, you'll either have to remove those eggs or keep up on treatment until all have hatched/been killed.
The easiest way I've found to dust the birds is to fill an old sock with the sevin (make a little powder puff), and the 'puff it' all up into the feathers, making sure you're getting it down to the skin. Really focus on the tail/vent area, under the wings, etc. I try to get everywhere but the head. I've found that if I grab a bird, hold them by both legs while they are laying on the ground, slightly lifting the legs but not dangling them off the ground, they quickly lay still, don't struggle, and I can gently lift them and roll them a little side to side and work the 'puff' up under all the feathers.
I had previously tried using one of the topical dewormers that I'd been told would treat them (didn't phase them), and an oral dewormer didn't do it, either. I dusted them, repeated in about a week or so, and all is good-- instant results. I dust the coop every so often as a preventative, and I dust the birds about half as often just as a preventative to keep any infestation from taking hold.