Dexron III is not a standard any longer. It is no longer a licensed fluid, with Dexron VI replacing it and it is suitable in the vast majority of cases for applications calling for Dexron III. While you still can obtain fluids claiming to meet DexIII/Merc, since it's an unlicensed fluid you really don't know whether it conforms to specifications.
Amsoil MTG is also a GL-4 manual transmission specific fluid.
The differentials will be happy with any 80W-90 or 75W-90 GL-5 gear oil. I don't think anybody except Amsoil makes a 80W-90 synthetic. You can obtain Mobil 1 75W-90 for cheap from Advance Auto Parts if you order online, use
discount codes then pick-up in store. I'd suggest a fluid pump to help fill the diffs/trans/t-case (search for W1139 on the AAP site). M1 75W-90 is an excellent fluid, I run it in my Pathfinder's rear diff (2WD

) and I'm happy with it. For the price and general availability, it can't be beat.
By the way, download the factory service manual
here and use it instead of the Chilton book. To save a copy of the FSM, right click -> Save As on every PDF, save them into a single folder, then use
fwd.pdf to navigate. The FSM is for a '94 Pathfinder, but the Pathfinder / Hardbody FSMs are interchangeable.
I hope this helps, good luck!