Old God's exist outside the circle of life and death. As long as they have influence they can be brought back to reality.Theis existence and power is somewhat directly linked to influence and followers etc. Would kind of refer u to the "American gods" series for a pop contemporary analogue. They cannot be killed per se. Titans tried to destroy them to avoid Azeroth corruption but Ysarjj effect had them think different methods. They contained them. Still if influence is strong enough they will rise. What we mortals do is defeating them and their minions but we will never kill them.
As for azerite the only thing I can work out from the cinematics is that the vast arcane power could be quite addictive much like the well was to elf's. Sylvanas knows, Anduin just got a taste