Oturmak is more for address. We prefer it if we want to ask where sb lives in a specific way. (İts the same ikâmet/sekene in Arabic.sorry if I mistyped)
Yaşamak is to show about living. So its general. We generally use it to ask cities or countries.
But oturmam and yaşamak are interchangable, you can use both instead of each other. There is no specific seperation. And oturmak is more used than yaşamak.
Kalmak is to spend the night(s) somewhere or to stay. For example Nerede kalıyorsun? Otelde. (İn the hotel, probably a bussines or holiday situation) or we can use it for example to ask a student if he has gone to another city to study. And he can answer as Yurtta kalıyorum. (I stay in a student hostel)
So kalmak is for short term stayings but oturmak and yaşamak is about to live or to reside.