The axles are just fine. They are both open differentials. An easy way to tell when on stands is that when you turn one tire by hand, the other side will rotate the opposite direction. Under power, only one tire will turn. A locking differential or limited slip will power both wheels. The front axle is rarely a locking differential, but can be a limited slip. When the front axle is locked, it is hard to steer, due to both wheels fighting to go the same speed. When you turn, one wheel travels faster then the other. On a non-power steering vehicle, having a front locker, is a good way to break a thumb if held inside of the steering wheel.

The transmission. It sounds like there is some rust in the top end of the transmission. Pull the top cover off the transmission and inspect both the shift fork and the shift cane for rust. Since you can only find 2nd and 3rd gear, it sounds like the intermediate shaft is rusty as well. This will cause the gears to be stuck on the shaft. Without looking up the information, it seems by memory, that 2nd and reverse share the gear, so if it will not slide, you will not have reverse.

The PCV valve on the side cover should be attached to the intake, and shouldn't be vented to the atmosphere. A little oil can be expected if there isn't a functional valve attached. With oil being within the compartment, a drop or few finding their way out wouldn't be surprising. Odds are, somewhere in history, someone thought the PCV system wasn't needed.

The fuel line isn't sealing at the flair, or the flair is cracked. Plumber's tape will not do any good. Check the flair to ensure that it is the right angle for the fittings. Check the fittings for scared surfaces that will not allow the line to seal.