Let's say I have 15 copies of Strionic Resonator for a total of 16 triggers and I attack with Ulamog, the Ceaseless Hunger and copy its triggered ability to exile 20 cards from the top of defending players deck. Can I choose a different player or players to exile from or does it have to be defending player's deck?
You cannot choose any other player than the defending player. Ulamog, the Ceaseless Hunger says:
Whenever Ulamog, the Ceaseless Hunger attacks, defending player exiles the top twenty cards of their library.
As you can see, there is no word 'target' in the ability. That means that when copied with Strionic Resonator, it doesn't allow you to choose another player.
The number of Strionic Resonators is irrelevant in this case. The ability works the same. You get more triggers though.