If it was mine, I would start with the tie-rods and drag-link ends. Remove them for a proper cleaning and inspection. All four ends are spring loaded and adjustable. The balls need to be round, so check that and the stems for any wear.
Next I would look at the king pins and wheel bearings. King pins require quit a bit of work and can be really tight or really loose coming out.
Wheel bearings need cleaned, inspected, greased and properly adjusted. Ball bearings require a different adjustment than taper bearings, so read the manual carefully.
Steering box would be the last item to clean and adjust, no need to adjust it when the other parts are worn. Yours likely has the steering wheel mounted off center causing the more to one side turning radius.
On a side note, my '37 always had a the steering wheel off center so I had an adjustable drag link made. The steering gear box needs to be dead center, if not it will have a loose feel to the steering. I don't no why my was off, never could figure out what was wrong.
Steering boxes are easy to rebuild build and adjust with the online manual as a guide. It to should be removed for a proper cleaning and inspection.
Last on my list would be spring bushings and shackles.
Tires need to be good soft rubber, old tires never drive right or non-radials. Radial tires don't follow the grooves like bias tires will.
With everything properly adjusted it will drive just as good as truck on the road.
