Despite the similarity of names, you could not have picked three bands that sound more dissimilar really. Here's my take...
I can't stand Wolf Eyes. I just find their music kind of disturbing in a fingernails-being-ripped-off kind of way. I think that's what they're going for, so I guess what they are doing is good if you like noise/experimental music, but it ain't my bag, baby.
Wolf Parade is rather good indie rock. Kind of a cross between The Arcade Fire and CYHSY (I expect I'll get flamed for that), but not exactly like either one. The general consensus of the forumites who attended their Black Cat show last month was that their album (Apologies to Queen Mary) was better than their live performance, but I thought they put on a very good performance, if not a great one, and expectations were too high.
Wolfmother rocks it old school style. RIYL Led Zeppelin, Black Sabbath. I haven't seen them live yet, but I've heard good things, so I picked up a ticket to their upcoming Black Cat show to check them out.