Is there a "Right" direction to build soffit with plywood?
Putting the sheathing to the outside makes hitting backing easier when hanging drywall, etc. On the other hand, it may be easier to hang the verticals pre-assembled if the sheathing is to the inside, as you can then screw through the 2-by into the joists unobstructed. From a structural standpoint it does the job equally well inside or outside. Do whatever makes sense in your situation.

OSB is more dimensionally stable than plywood (so you're not fighting warp while you build), and it's usually quite a bit cheaper. For this purpose 7/16 or 1/2" is more than adequate as the drywall adds support as well.