And they usually aren't standard power chords which sometimes makes in tricky to figure them out if I'm playing by ear. If you run into a chord your not familiar with what do you guys usually do to try to figure it out?
I hardly listen to anything with just power chords. I'm used to listening to and writing music with odd chords and odd tunings. Try listening to and learning more songs with odd chords so that you aren't stumped the next time you run across one.

It was the only task I would undertake...

...to reap the harvest that was mine

- [ P R O G - H E A D ? ] -
By definition, there's only really one way to express each power chord, unless you're referring to different fingerings, voicings or octaves. Are you just referring to odd-sounding or relatively uncommon chords in general?

The approach I would adopt would be to attempt to figure out the root note, if possible, roughly guess what kind of chord it sounds like and then test each of the questionable notes with the MP3 or whatever, in order to see if that note's actually being played.
If you have a decently good knowledge of theory, you can figure out major/minor/diminished chords. Take the chord that sounds most like the one you want to play and mess around with it until you get it. I assume you're talking about learning by ear; if so, the only way to really do that is to practice listening to various chords and learning how each one sound. It isn't that ignoble to look at a tab to see if they agree with you on a certain chord.