The One and the Three

[Tirinor]

When the One Ring was tossed in the Cracks of Doom how is it that Sauron was any less powerful than he was before? He wasn't in possession of the Ring during his Third Age stint in Mordor, he did much without it. Yet as soon as it's tossed, he is forced from Mordor, his minions scatter, etc.

Sauron is powerful without his ring because the ring is still "alive and well." He loses his power when the ring is destroyed because the ring is a container of sorts for a good portion of his power. It's as if you lost your car and your heart was inside. while your car was lost, you wouldn't be able to use it, but if it was destroyed, your heart, being inside the car, would stop working and you would die, or, in Sauron's case, be reduced...

And if the answer to my second comparison is "because the Ring and the Dark Lord are one" then doesn't that answer the curious question of diminishing Rings?

no. not the elven rings.