Disclaimer: I'm British, our definition of insults tend to vary from American ones.

Jerk seems more incidental to me. If a guy is just acting like an idiot and doing stupid things that irritate me, he's a jerk. Dick and asshole feel more like there's been deliberation behind whatever it is they've done. Like, if I was dating a guy and he cheated on me, he wouldn't just be a jerk, he'd be a dick because he was deliberately slighting me. I'd also be more like to call him a bastard - again, because of the deliberate intent behind whatever he did.

Perhaps asshole is more like consistently mean?