Can Strionic Resonator re-direct Ulamog, The Ceaseless Hunger's exile ability?
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.