Mis-aligned differential splines HELP NEEDED
You may have to end up taking it back apart. The correct way to assemble them is with the axles installed IN the third member BEFORE you tighten down the case halves. Tighten down the bolts slowly and with HAND tools gently shaking the axles as you tighten to keep the side gears centered as best as you can. Once you get them hand tight and the axles will slip in and out easily, torque the case bolts to spec and then remove the axles. I assume you know to use red locktite on the bolts.
Sorry, but if you cannot break them loose with a pry bar, that's the only other way.