You can take the frame to a good bike shop or framebuilder and ask them to check the alignment. They should check that the dropout faces are parallel and in line, and that the stays are properly centered on the bottom bracket. There are standard tools to check this.
One thing you can check on your wheel. Take out the quick release skewer with the wheel in the bike and see how much axle protrudes into the dropout. The axle end should not be flush with or protrucing past the outer face of the dropout, but recessed inside it, yet long enough to be supported by the frame. If the axle were too long, then the quick release would not hold it in place and the wheel would slip as you ride and apply pressure to the pedals. Different frames can have different dropout thicknesses, and 70s bikes sometimes had a thick derailleur hanger on the derailleur that effectively made the dropout much thicker. If the wheel you just put on originally came from such a bike and the new bike has the derailleur hanger on the frame, or just has thinner dropouts, this could explain the problem, and the fix is easy. You'd either have to move both cones to change the axle spacing outside the lock nuts, or cut the axle shorter with a hacksaw.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72