Sounds like it could be a combination of several things. I'd start with tie-end rods, and king pins and bushings. Might even take a look at the play in the steering box, if any, and even the wheel bearings although not likely.
Most can be checked by lifting the vehicle and grabbing the wheel top and bottom... and left and right..and then shake/pull on them up and down, side to side. Sometimes you can tell if tie end rods are bad by grabbing them right tight and twisting/wiggling them around.
Much has been said about the sway bars but I think most agree it does help.... especially on the panels/burbs but even without them you should not be having the problem you mention. I owned a 50 model several years ago and after the tie ends and the king pins it drove very well.


1937 Chevy Pickup
In the Gallery
1952 Chevy Panel
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1950 Chevy Coupe
Pictures!

I'd rather walk and carry a Chevy hub cap than ride in a Ferd.
I can explain it to you, but I can't understand it for you smile