steering box is probably worn out. and the bad tires in the front only make it worse.
also, tell us about the front wheel bearings. new? old? how were they put together, and how tight?
they should be packed about 1/2 full of grease, and installed. run them in finger tight then slightly tighten a bit more making sure the wheel still spins freely. and absolutely install new cotter pins so they cannot loosen up.
if you just run them finger tight and forget the little extra you will get sloppy steering/tracking. if the old front wheel bearings are worn out, same deal.
found you a decent article about the front wheel bearings:
http://www.popularmechanics.com/cars/how-to/maintenance/4205243