If you put the same main CV parts back on as you took off (The joint and axle itself), maybe you have a bad wheel bearing(s); it's the only part that would have shifted, as the CV joint and wheel hub are just two big pieces of metal. This especially could have happened if you rolled the vehicle around with no axles when you had the drivetrain out, because the bearings need side loading from the axles to remain tight. This also might be the reason why the passenger axle interferes with the control arm, as the wheel bearing might be 'sagging'. Also, since you don't have the front or rear mounts torqued, the drivetrain is going to tilt back due to it's weight, causing the rear diff flanges to be lower to the ground and, by extension, the control arms. Is the car on jack stands?
Also to damac: The reason the axles locked up is probably because the rebuilders that 'made' those axles put on some post-1986 outer CV joints, which have a shallower taper on their outer joint housings which cause them to hang up on pre-85 cars. Nowadays rebuilders just slap together whatever fits and get their money; the price you pay for overseas labor. I