I recently bought a used truck from an auto lot. I had it inspected the next day (it seemed fine and no lights or visible leaks when I bought it), and it was found that there were several major leaks in the transmission input/output seals, pan gasket, and rear differentials, and engine oil leaks in the back. I tried to return the truck, but the auto lot owner declined. I would like to know whether I should replace the gaskets, or the transmission itself? It seems like there could be an issue with the transmission given the amount of leaks

 

Welcome to the forum

Manual or automatic transmission?
2.3l, 3.0l or 4.0l engine?

Reads like rear main seal of engine could be leaking, but that's usually a very noticeable leak since its a pressure leak, not just a drip leak like valve cover or oil pan

Is the transmission misbehaving?
At 160k miles an automatic would be nearing the just rebuild it territory, approx. life of an automatic is 250k if well maintained, and you probably don't have that history
It would be prudent to have a trans shop have a look and do a pressure test to see if just a Valve body replacement would get you the remain 90k from the bands and clutches

Rear axle leak can be simple or complicated, it could just be blown oil, from the engine/trans leaks so not a rear axle leak
Or it could be rear cover leak, Ford didn't use gaskets on these, just RTV, not hard to redo the RTV or add a gasket
If front of rear axle is leaking that's called a Pinion Seal leak and the axles and the "guts" of the differential have to be pulled out to change this seal, then everything needs to be re-shimmed on reinstallation
Also axle seals and bearings changed, just because axles are out

 

It’s a 2003 Ford Ranger 3.0 RWD V6. The transmission seems mostly smooth; I haven’t had any problems shifting or anything. Firestone recommended I replace the main bearing oil seal, valve cover gasket, and transmission seal kit. I’ll see if they can pressure test it for me.

Thanks for the comprehensive response.