On the 1980-81 4 cylinder X cars, and all V6's, the 2 barrel Rochester Varajet carburetor was used. For 1980, the carburetor was known as the 2SE- it had no electronic controls on it. From 1981 on, the E2SE version was built- several carburetor functions became controlled by the ECM computer.
This carburetor was designed as a 2 stage down draft type, which allows for reasonable economy when crusing, yet a second stage allows for better performance when required.
These carburetors are generally pretty reliable. I have seen a lot of older versions with choke problems, though. As with all carbureted vehicles, periodically, the tang connecting to the choke coil becomes disconnected, or the coil itself becomes loose and does not hold the choke closed when the car is started cold. This can cause the car to be hard to start when cold, or cause rough idling until the car warms up. (If your car is doing this, and you want to fix it, see notes on how to do it below.)
I've also seen the vacuum break mechanism (which pulls the choke off a fraction of an inch when the car starts) fail once in a while. This causes the choke plate to be held shut when the car starts, causing rough running. Funny how most of us have forgotten about these kinds of problems now that most cars are fuel injected. If your car stalls, and then fails to start when the car is cold, or idles roughly when the car is cold, check your choke mechanism and vacuum break mechanism(s) (1 vac. break on the 4 cyl, 2 on the V6).
Yet other than these problems, the 2SE/E2SE has few problems, which is good considering that it is a relatively complicated piece of equipment designed to be low polluting and fuel efficient. On the E2SE, the computer controlled perameters are: the idle mixture (controlled by the idle mixture solenoid); on the 4 cylinder, the idle speed (controlled by the idle speed motor); and on V6s, the throttle position sensor (TPS) is also incorporated into the carburetor body.
The throttle body fuel injection system (TBI) used on the 1982-85 4 cylinder models helps prevent cold start problems from occuring. I'm not overly familiar with this particular TBI system so I will not elaborate on it here. However, one noteworthy change on the 82 and later 4 cylinder engines was the addition of an electric fuel pump to work in synch with the fuel injection system. I know the early TBI units were called the 300 series or something. The later GM cars (late 80s & 90s) had a 700 series TBI, I think.
MPI
A few (VERY few) 1985 2.8 V6's came with multi-port fuel injection. This system is TOTALLY different than the TBI system used on the 4 cylinder. The TBI system is basically the bottom third of a carburetor (the throttle body, with the air horn and fuel bowl left off) and an overhead fuel injector. This means fuel is flowing through the intake manifold like on a carbureted vehicle. MPI has fuel rails with ports which inject fuel directly into the cylinders. Thus, only air is flowing through the intake manifold. MPI cars with a given engine will have more power than carbureted or TBI cars with the same engine, because the intake manifold can be designed for better air flow. Also on carbureted and TBI cars, the intake manifold must be designed to keep the fuel suspended in air, and such manifolds don't give the engine as good breathability as on MPI. Also, when the manifold/engine is cold, fuel tends to condense inside the manifold on carbureted/TBI cars, whereas MPI doesn't have this happen. Despite all of this, carburetors and TBI are easier to diagnose and fix, and are much lower cost to repair than MPI. Also, if you have a problem with the ECM, the car will keep running; MPI is totally dependent upon the computer for the car to stay running.
Nearly all the X cars came equipped with the 3 speed Turbo-Hydramatic automatic transmission (THM-125). This transmission is really a "transaxle" - since it powers the front wheels of the car. The differential is located inside the transmission. This transmission was produced for use in the X body cars, and has been the only 3 speed automatic ever used since. It is extremely durable- much more so than its successor, the 4 speed THM-440 (which was never used in the X cars). As per GM tradition, the THM-125 is a smooth shifting 3 speed. The shifts are controlled by a TV (throttle valve) cable, which is hooked to the throttle lever, rather than using a vacuum modulator like on many rear wheel drive GM cars.
Also available was a 4 speed manual overdrive transmission. This allowed a 4 cylinder X car to achieve 40 mpg on the highway. Most Skylark & Omega buyers did not buy their cars with this transmission.
1n 1983, X cars with the V6 engine (and maybe some of the 4s too, but I'm not sure) began to use the THM-125C transmission. This transmission has a mechanically engaging clutch on the torque converter which gives a "solid" connection between the engine and the drive wheels as compared to the traditional "fluid drive" type transmission. This torque converter clutch (TCC) allows for better fuel economy at higher speeds. At about 40 mph the clutch engages and allows the engine to turn at a lower rpm, thus yielding more mpg's. When it engages, it may feel like an extra transmission shift. On most cars its engagement is so smooth you don't even feel it, though you may feel it coming on and then off again when you step on and let off the gas pedal while cruising.
Sometimes these had a problem with the TCC getting stuck on. When this happens the engine will bog down and stall when coming to a red light. Replacing the TCC solenoid will permanently fix this problem, though it can be temporarily fixed by just disconnecting the connector at the transmission (though you will notice the engine revving higher at highway speeds).
In early X cars, 3 different differential gear ratios were used in the transmission. There was an economy 2.53 ratio (which I imagine must only have been used with the V6), a 2.84 ratio (very common- most all 125s had these), and a 3.1 ratio (used in 80-81 model years only, I believe). The differential is special in that it is a planetary design differential, which is distinct from other helical or hypoid design differentials.