As Nihiloor's first triggered ability resolves, you choose up to one creature for each opponent, and tap them all at the same time. Then, a separate triggered ability is put on the stack for each creature you tapped this way. Those abilities are placed on the stack in the order you choose. If tapping those creature caused any other abilities you control to trigger, those are also placed on the stack at this time.

Both the tapped creature's power and the target creature's power are checked both as you put the ability on the stack and as the ability resolves in order to make sure the target is legal.

If the tapped creature is no longer on the battlefield as the trigger resolves, use its last existence on the battlefield to determine whether the target is still legal as the ability resolves.

If Nihiloor leaves the battlefield before its enters-the-battlefield ability resolves or before its reflexive triggered abilities resolve, then you won't gain control of any creatures.

If a creature you tapped for Nihiloor's ability is somehow no longer tapped as the reflexive triggered ability resolves, that ability will still resolve and you will still gain control of the target as long as it has less power than the creature you tapped.