I think you are looking at a compressed overdriven sound as opposed to a distorted sound. The easiest way to get this is with an overdrive type stomp box, check out the boss US website they have a lot of info about the different types of useable distortion there.
My instructors page and www.studiotrax.net for all things recording.
my toons Brought to you by Dr BadGAS
my toons Brought to you by Dr BadGAS