Thought about it for the electrical hazard that is the pet store I work in.
Simplest way, imho, is to get yourself a small chunk of rounded PVC and cut it into about 3 pieces (to get a small 'C' shaped piece), and mount that on the wall directly above the outlet. Any splash from above will get diverted, and the rounded shape will ensure no puddles form. And if water splashes from the bottom or directly from the side.. Well.. You should probably be more careful than that.
You could always go and buy yourself one of those waterproof electrical boxed for outdoor use, but wiring that thing in would be a huge pain.
As for the unused outlet - you know those childproof outlet plugs you can buy? It's just a plastic plug, essentially. I'm sure if you found a thin weatherstripping foam/rubber and sandwiched it between the plug and your outlet it would make a pretty clean seal.
Barring that, if you don't mind residue, you could simply take over that outlet with duct tape.
Any better ideas for the in-use outlet? I could certainly use some suggestion myself.