My previous house was built on an ant-hill- we only found this out of course after we moved in!
Luckily it was mostly the kitchen they came into and they were easily spotted.
The key is to locate the nests. We found lots of them outside near the paving and at the grass edges, because they built little waste piles of sand to show us where they were. I used a variety of methods to destroy the next, including boiling water, which seems harsh.
Another method was to use splenda, canderel, or other supermarket sweetener that looks like sugar. Sprinkle some around the nest site and they'll head for it, not knowing their bodies aren't designed to absorb the chemicals, and take it back to the nest.
If you do this whenever you spot them they will soon move elsewhere.
I agree they can give a nasty bite.
I think flying ants are just ants that have grown wings later on but I'm not an expert on these things- just killing them!
Since I moved to a new house I haven't seen a single ant here in five years! Hope I haven't spoken too soon.
Good luck.