As has been said up thread, there's nothing inherently wrong with straight axles. Big trucks use them and roll along at 80 MPH legally in some western states.
They ride rougher in part because the sprung/unsprung weight ratio is somewhat less favorable when one wheel goes over a bump and much less favorable when both wheels do. And as most of them have leaf springs, there is resistance within the spring pack adding to shock being transmitted into the frame. That's a door that swings both ways, enough resistance and there's no need for additional damping. I drove 50s/60s Kenworths and Peterbilts with no shocks anywhere. But the KW torsion-bar rears did have shocks as did the Pete air-leaf rears. Rear shocks on my 1-ton were an option mine didn't have. Loaded it was fine. Unloaded it bounced a lot. It now has rear shocks. My 50 Studebaker had the rear leaves encased in metal jackets with grease fittings. Greasing the springs made a noticeable difference.
Adding a rear swaybar will correct oversteer when loaded as will increased spring rate. Adding a front sway bar will correct understeer, likewise will increasing the spring rate. Adding caster will make the steering return to center quicker but make for heavier steering AND the rig will tend to follow ruts and such in the road. Radial tires will make it much harder to park unless you have power steering.
Changing the wheel offset to more outboard centerline changes the scrub radius and will also cause the rig to follow ruts. Changing the wheel offset also changes the effective spring rate, particularly on independent suspensions but to some degree on a straight axle in a turn or when one wheel hit a bump. Adding wider wheels to accommodate wider tires will change the offset by 1/2 the increase in wheel width.
