[Veritas]

Sauron made the rings, but in one of them, the one ring, he put all his power. The other rings were having less power, but still powerful.
Without the one ring the other rings were having power, but less, because Sauron put some of his power in the rings.
The powers that hte one ring 'awakened' in the others rings, the elves used it to be immortal, I don't know how they used the power, an interesting question, but when the one ring was distroyed, the power that it awakened in the other rings would fade out, and the rings would be magical, but could not give power enough to let the elves be immortal in Middle-Earth, that's why they moved to the west, at the end of the third age.

I hope I answered your question, but there will be enough replies further.