Hmm… okay, I’ll try to answer this.
[Tolkien geek hat on/]
The elves still have three rings of power- Galadriel has one, Elrond has one, and Gandalf has one. Elrond’s ring, which I believe is called Vilya, although I may be mistaken, is invested with power over the forces of water. This is how he was able to summon the river to wash away the Ringwraiths at the ford when they’re chasing Frodo. (With Arwen in the movie, although with Glorfindel in the books. Yes, that Glorfindel.) With this, he can do many wondrous things, although we’ve never told exactly what. We can only assume it’s really cool.
Gandalf has Narya (again, I think) the ring of fire. This is why he says to the Balrog in Moria, in both book and movie, that he is a “keeper of the secret fire”. I believe that’s what he’s referring to, although he could mean the Eternal Fire somewhere in the Void which Illuvatar set up and Morgoth once tried to get hold of, but we won’t worry about that right now.
Galadriel has Nenya (?), the third ring. Pick an element, I’m not real sure. Apparently, she’s using it to protect Lorien and somehow slow time in those woods. Elrond may be doing the same with Vilya in Rivendell- several references are made in the books as to how time passes strangely or not at all in both of those places. (See my above post about the elves’ fear of the passage of time.)
So all the elven rings can apparently do pretty cool stuff, although it’s vague as to exactly what they can do. It seems they’re mainly used to keep things relaxed and groovy in the elf community. If Sauron gets his hands on the One Ring, he could control the actions of the other three rings. Their power would be subverted to his purposes, no matter what the bearers tried to do with them. Obviously, if that had happened, G, G, & E would most likely have gotten rid of the things- their power to do good would have been destroyed. Sauron does not seem to be able to corrupt the bearers of other rings except the nine kings of men who became the Nazgul. They were corrupted because of their greed and lust for power, which elves apparently don’t have. (Although this is completely contradicted in The Silmarillion.) I say this because while the men were corrupted, the elves, despite possessing their rings while Sauron originially had the One, continued to fight against him.
If Sauron had gotten his hands on the One again, it really wouldn’t matter who had the other three, or even that they existed at all. Their power grows weaker as time passes, and would have been destroyed by Sauron’s finding of the One. Not that such trivialties as one’s jewelery would matter much in that event.
But the ringbearers know what Sauron is doing, sorta, before anyone else does, because their rings and the One are connected, and Sauron’s essence/life force/kami/will is tied to the One Ring. They’ve all seen the Eye.
On to Valinor. Valinor is the elves’ ‘ancestral home’, located far across the western seas in the land of Aman. It is here that the Valar (sorta angels or lesser gods in Tolkien’s mythology) live and watch over the world. Everything is deeply relaxed and groovy here. This is where elves generally end up after they die and do their stint in the Halls of Mandos. (Purgatory, if you will.)
Galadriel’s banning from Valinor was never firmly established- Tolkien revised this part of the story many times. Here in a nutshell, the story:
Back in the day, lots of elves lived in Aman with the Valar. All was well. The lights of the land were not the sun and moon, but two magic trees. One of the Valar rebelled against Illuvatar, Creator of the Universe, in a Lucifer-ian manner. This was Morgoth. (Sauron is a minion of Morgoth.) Morgoth poisoned the Two Trees; the light started to go out. But wait! An elf named Feanor, a great craftsman and smith, had made magic jewels called Silmarils, in which the light of the trees was caught. But Feanor was prideful and arrogant and greedy, and refused to give up the Silmarils. He made an oath that he would kill anyone who tried to take them. But Morgoth stole them and ran away and wreaked havoc on the lands to the east, which were called Arda, or Middle-Earth. Feanor vowed to retrieve them, although for his own purposes. This, coupled with Morgoth’s bad mojo, turned the Silmarils evil, and anyone who wanted them became evil. (Notice a recurring theme here?) Feanor attempted to follow, and he dragged the Noldor with him. (Noldors were just an elf population, mainly related, and mainly living closest to the Valar.) The Teleri, elves who lived by the sea, wouldn’t give the Noldor their ships to cross to Arda, so Feanor took them by force and killed a bunch of the Teleri. This was the Kinslaying, the first time elves had killed other elves. The Valar were horrified, and banned the Noldor from ever returning to Aman. (The ban was later lifted due to continued good behavior by the Noldor in opposing both Morgoth and Sauron.) Feanor & Co., including Galadriel, show up in Middle Earth. Many battles ensue, treachery, intrigue, romance, etc. The Silmarils end up being destroyed, Morgoth gets sent to the Outer Darkness forever, more people die, and then everything sort of quiets down for a while. Meanwhile, Galadriel has other adventures, none of which have anything to do with the plot of LotR. She ends up founding the kingdom of Lothlorien, marrying an elf named Celeborn, with whom she has Celebrian, Elrond’s wife and Arwen’s mom. (Celebrian had already returned to Aman by the time of LotR. There was some…unpleasantness involving orcs.)
The elves begin to leave Middle Earth, as their time is over, and the world must pass to the control of men. Galadriel still stays behind. Tolkien originally wanted her to be especially banned, because she was related by blood to Feanor, but he never really decided. His letters and unfinished manuscripts mention the story of Galadriel in a few different forms. How Galadriel got the ring Nenya, I completely forget.
[Tolkien geek hat off/}
I can’t find any of my books, so this is all off the top of my head. If more astute Tolkien geeks notice mistakes, please correct them as needed.