Elven Rings and the One Ring
 

Maybe I'm missing something, but in all of the times I've read The Silmarillion and The Lord of the Rings, I haven't been able to figure this out.

Celebrimbor made the 3 Elven Rings of Power, without of Sauron's knowledge or any of his power. So, why were they diminished when the One Ring was unmade? I'm unsure of how their power was dependent on the power of the One in any fashion.

As Tolkien says in The Silmarillion: Of the Rings of Power and the Third Age:
Sauron made the One Ring to rule all of the others, not just those that he personally had a role in making, as is made clear in the above. In fact, the holders of the Three Rings knew instantly that they were in danger of being controlled as soon as Sauron put the One Ring on, so the connection there was quite clear....

I guess I'm unsure as to how he could encroach on those rings he had no hand in making. The 7 Dwarves' and the 9 Mens' rings, he actually touched. But he never laid hands on, or had any role at all in making the 3 Elves'.

It seems to violate the "norms" of fantasy magic, I guess. And it's never clearly explained.

Perhaps because it was "similar" magic used to make the Elves' rings that Sauron's control was "in tune" with them, even if not exactly in tune?

Tolkien wrote before most fantasy. And unless I'm mistaken, Tolkien was, so to speak, the kick-off for a great deal of what fantasy is out there.

But he did have a hand in their making. The Three, though never touched by Sauron and physically made by the Noldor of Eregion, could not have been crafted without Sauron's aid. Being at least partially the results of Sauron's knowledge and instruction was the reason they were ultimately under the dominion of the One.

As Inziladun said, the smiths of Eregion learned the craft of making rings of power from Sauron; thus, he knew how they worked at a very fundamental level. It was said, of the inscription on Sauron's ring during the Council of Elrond, that when Sauron finished forging the One Ring, he spoke the words of the ring-verse, which the smiths of Eregion heard and "knew they had been betrayed." If the speaking of those words was enough to constitute a betrayal (which also prompted the Elves to immediately remove their rings), it would appear that it was actually the "spell" by which Sauron sealed the plan which he had initiated when he went to the smiths as Annatar and taught them this craft. Celebrimbor was able to make the Three useful in ways that did not have the corrupting influence of those rings Sauron helped to forge, but he apparently could not avoid incorporating aspects of the basic "blueprint" of which Sauron was able to take advantage, rendering them useless so long as he held the master ring.

And Sauron clearly did have knowledge of their making. The words of ring verse are what the smiths heard when Sauron "activated" the One Ring, Sauron spoke them, and the full verse mentions the Three. Since the elves who held them took them off the instant they knew of their betrayal, they were not used and Sauron did not know who had them; he tortured Celebrimbor to death, trying to force him to reveal that secret, which he kept till his death. But it seems apparent to me that Sauron knew of their existence, both before and after he finished the One.