Your title says you have a 736 Berkshire. But the chassis pictured above is from a 1947-1949 726 Berkshire.
Some of the parts, such as the wheels and axles are different between the two. I'd have to check, I think the worm gear may be different too.
Lionel never sold wheel cups that would fit a nickel rimmed Berkshire wheel. As far as I know, Hobby Horse is the only outfit that made the proper cup.
Judging by the appearance of your chassis, I'd guess that at least the faces of your axle bearing are worn. I'd suggest doing one of the following:
1 - replace the axle bearings
2 - put shim washers on the axles between the wheels and the axle bearings. I typically use 671M-19 or 671M-23 washers.
