sounds like lice to me! i just had a kitten with lice recently. Revolution will take care of that as will Frontline Plus. Revolution specifically says it will kill lice, but Frontline worked jsut fine too. The best way to get the eggs of after treatment is to either let the fur grow and they fall off or else shave the fur down where the eggs are. These are egg SHELLS by the way, not an actual egg with something inside. IF you look closely on the cats fur in those spots, you can see little tiny brown specks that are moving. That is the lice. Treat with the topical medication from the vet and you won't see them anymore but the eggs won't come off no matter how hard you wash or scrub!
Also, you will not get lice from the cat. But for the sort of creeiness factor, I would confine the cat until the lice is gone. It is extremely contageous to other cats so treat all the cats in your house. Might want to keep your outdoor cat on a monthly topical because she got it from outside, she will probably get it again.