I just want to pass on my sympathy!
We had the same problem - teeny tiny ants, so tiny they look like dirt, until you look closer and realize the dirt's moving.
We found out that they're called "Pharaoh Ants", and they're attracted to protein and grease. They're also different from other ants, in that they have multiple queens and if you put their community under stress they'll actually split up and send queens out and each queen will start a new community. Standard spraying and dusting can make them worse, because they'll just scatter.
They can get into containers that we'd normally think of as "sealed" - like peanut butter jars with the tops closed tightly! They walk right up the screw top, around and around, and get into the jar, no problem. It was not a great feeling when I opened up my jar of peanut butter and found it black with the little b@st@rds. They also like breakfast cereal. My poor son ate most of his bowl, before realizing that the black bits floating in the milk weren't granola. His sister STILL teases him about it!
Wikipedia recommends boric acid baits, but what worked best for us was putting all our food (except the stuff in unopened cans) inside the fridge (they're tropical, so they can't take the cold). And then I'd spray them with Lysol spray and scrub any areas I found them in. After which I'd leave a coating of Lysol on the surface for awhile. I also sprayed all the baseboards with Lysol, and anywhere else I thought they might be coming in.
It seemed to work, as I haven't seen them in years. We've also had the house lifted and a basement poured since then, so the construction probably destroyed whatever was left of their nests.
Good luck!
