Acceleration/Deceleration steering pulling.
My roommate has a 2004 Grand Cherokee Laredo v6 selec-trac. I've driven it and especially after buying my 2002, the steering pulling one way then the other when accelerating or decelerating has become more apparent. My guess was worn engine mounts that moves when the torque of the engine changes.
But comparing how the two of our Jeeps drive, his seems to need an alignment. I don't think that a bad alignment alone would cause it to sway while driving like that.
2002 Jeep Grand Cherokee Limited V8