Where are you living? Most houses in most countries will have 3 prong power-outlets (here in Japan they don't
).
If the outlets have 3 prongs, then chances are the house is grounded (or you'd hope so anyway).
One tip to avoid ground loops (so I've read - I'm no expert), is to run your monitors and your mixer off the same out let. Because I had to make my own grounding setup, all my gear grounds off the same line.
Your soundcard is the biggest problem by the sounds though.
Not sure if eliminators will take something away from the signal - never used them myself.