The power of the 3 elven rings are fairly easy to spot. Elrond uses Vilya to summon the flood, that drowns the Nazgul's horses, so he uses it as to protect Rivendell. Galadriel uses Nenya to sustain Lothlorien, to keep it "alive." That is why when the one is destroyed, the three lose their powers, meaning Galadriel wouldn't be able to sustain Lothlorien anymore. Gandalf, I'm not quite sure, might have just been able to enhance his physical power, example when fighting the balrog.
The 7 and 9 are a little more difficult.
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