Hmm. There's not much info about lice in African-American hair because it is not commonly seen in African-American hair due to the shape of the hair shaft. (See an earlier post about this here.)There are those that say that African-American people don't get lice, which is not true. Cases are uncommon, but lice are very good at adapting and I am sure that we will just see more and more cases of lice in this population.
In your case, are you sure you actually have head lice? You say you haven't seen any live lice and the what you think have been nits have fallen off easily, which doesn't really happen. Nits are glued to the hair and have to be scraped off the hair shaft with a good lice comb or with your fingernails, so if something is coming off with just a flick or a light rub, I would guess that it is just dandruff. Also, you really need to see a louse before you can be certain you have an active case of head lice. Lice are small but not microscopic (though I really enjoy putting them under a microscope!) They are usually a mousy brown colour but can look darker in light hair and lighter in dark hair but are also sort of translucent and can blend in with many hair colours (which is a pain).
But let's assume you are dealing with head lice. So what to do? It truly is more difficult to get a good lice comb through very curly and coarse hair. However, I have done it by wetting the hair and using almost an entire bottle of the cheapest hair conditioner on one head when combing - you may not need to do this, just use as much as you need. You don't rinse this out, you comb through it. This can help to make the hair straighter and detangled for combing. (You first need to detangle with a brush or a wide-toothed comb before you start with a lice comb.) Unfortunately, combing through tight curly hair is more time consuming, quite messy (I recommend you climb in the bathtub with your own kids for lice combing when you need loads of conditioner - the water and bath toys help keep them occupied). It becomes more difficult to see what you have combed off the scalp when you are combing off globs of hair conditioner, but it can be done. After combing, wipe your comb on some toilet paper and look through the conditioner for signs of eggs or bugs.You may need to try out different metal lice combs to find one that works for you that doesn't pull out your hair. Do not comb the hair unless it is wet and coated with conditioner. Hair conditioner is better to use than other greasy products like olive oil because the grease can actually grab at the comb, where the hair conditioner will allow for a smoother and more continuous stroke from root to tip.
Even if the combing is tough, keep trying. If you have tried different metal combs and have been doing wet combing with conditioner and you still find it too hard, then you can try wet combing with a plastic fine toothed comb. Plastic combs generally do nothing in the way of removing nits and very little to remove nymphs, but they can still remove many larger bugs through wet combing with conditioner. And if you can't comb out everything, it is still better to comb out something. If you keep combing thoroughly and regularly (every couple of days), the idea is that you will be able to comb out the bugs as they hatch but hopefully before they can lay new eggs allowing you to outrun the problem. As for nits, if the metal lice comb is too painful, get yourself in good light (I recommend using a cheap head lamp for nit-picking) and pick out anything you can see. Focus mostly on anything you see right next to the scalp. And, if you are not sure about what you are seeing, when in doubt, pick it out.
Lastly, read about the use of an ordinary hair dryer as a lice-fighting tool in other posts on this blog. There is research to show that fast-blowing warm (not hot) directed air blown on sections of the hair and scalp can dry out most of the nits and about half of the bugs. Use the blow dryer on dry hair on the highest speed, but don't burn your children with the highest heat. I like the use of a blow dryer because, like a good lice comb, it is a tool you can use again and again. Read the posts for more info and check out the research.
As for lice shampoos, I personally don't recommend them but only because of their limited (or non-existent) effectiveness, the false sense of security that they give, and their extra cost. As for house cleaning and laundering, I DO NOT RECOMMEND that you do any extra cleaning. There is no research to show that this helps in any way and research to show that it has no effect (again, check out the research links on the blog). I have much experience to show that parents who focus on the surroundings more than on the scalps burn themselves out and make themselves nuts over these ineffective, busy, and costly tasks. Keep your focus on the head. You've got enough to do with the combing, picking, and blowing. Try to maintain some balance, keep things in perspective, get some sleep, and stick with it until you have had 2 weeks with no new sightings.