usually if one of the cv joints is worn it will cause a vibration, worse on acceleration in a turn to the side with the worn cv joint. you can check by hand, jack up the car and than rotate the outer cv joint back and forth, there should be little to no play in the joint.
if you have a leaky axle seal, that might indicated the outer diff bearing is wearing out, allow the axle stub to wobble too much and cause it to leak past the seal. This can also be a source of the vibration.
I have the same thing right now, and I replaced the cv axles (and all other worn suspension parts) but the vibration is still there, so I am thinking it is in the diff now. Will have to replace the whole assembly, or consider replacing the bearing in it, which means setting up the shims to reset the gear lash between the ring and pinion. I would rather just replace the whole assembly.
So first check the easy and less costly things: cv joints. Replace if bad. The seal might be just a coincidence (which go bad sometimes even with good diff bearings). if it is good, than see if there is any play in the axle stub where it plugs into the diff assembly. If so, you may need to replace the front diff assembly, if so be aware that there are two different front diff ratios for the manual trans Tercel, '83-84 has 3.73:1 and '85 and later has 4.1:1. so you either have to match it, or also replace the rear diff with the matching ratio.
'87 Tercel 4wd SR5 (current engine swap project)
'84 Tercel 4wd (daily driver, with on going mods)
'92 Mazda MPV 4wd (wife's daily driver)
'85 Tercel 4wd DLX auto(daughter's daily driver)
'01 Honda Civic (other daughter's daily driver)