Here's an article that describes the life cycle of fleas and ways to fight them:
http://blog.deanandadie.net/2008/09/a-house-infested-with...
It sounds like living in GA would be the perfect environment for fleas to live because they like warm weather and high humidity.
Are you sure you are picking up the fleas from outside, or have they settled into your house? To get them out of your house, this article suggests vacuuming thoroughly twice a day for a certain number of days in a row can work. If you are carrying them in yourselves from outside, that seems like a harder problem. You might talk with your vet about a different yard treatment, as it sounds like fleas become resistent to pesticides very quickly and the one you've used might not be working.
If the cats in your neighborhood are really strays, can you call animal control to have them captured? If they have owners, then they should be treating the fleas also.
Living in Minnesota, I haven't had this problem, since our cold weather kills them!