Powers of Isildur
 

What powers did Isildur have to curse the oath-breakers?

I think the fact that they broke their oath and Isildur condemned them for doing so was enough, and Isildur didn't have any special powers. It's a common theme in fantasy. One breaks an oath - one lives forever as a ghost, unless he fulfills his oath.

(I suppose this is what you meant)

yea, you can relate it too the natural magic of elves.(if you wish)

Isildur didn't necessarily have to have any "Elven" powers.

In Anglo-Saxon society, the King/Leader was the ultimate authority. All warriors and citizens had to pledge fealty to him, and had to follow his every command. If they went back on their word, they would be considered traitors of the worst sort. Since Tolkien based much of Middle-earth on Anglo-Saxon society, I'm assuming that the same principles hold. Isildur had the right of the disobeyed leader to curse the traitors, and more often than not, when one has the right to do something, one has the power to do that "something." In this case, it was cursing.

Yeah I never though it was any sort of magic spell, just the power inherent in a great leader.