What is wrong with a Lego pneumatics system that won't go? I own a LEGO Technic Unimog U-400 (part number 8110) and have been very pleased so far with the performance of its pneumatic system. However, after storing for just a month or two (after a good 5+ months of hard use), the pneumatic actuators in the crane did not work, even with brand new batteries. I disconnected all of the hoses and felt that the actuators had more friction than they had previously had when the model was working well, which led me to oil them with vegetable oil, along with the pneumatic piston pump.

When I reconnected all of the hoses, switches, connections and tried it out, the second actuator (the one controlled by the middle switch) and the third actuator (the one that powers the claw) still didn't work, while the first actuator (the one controlled by the first switch from the left) worked as good as new. I have checked and double checked the connections. What is the problem
 here and how can I fix it? Apologies for bad grammar and/or bad formatting.

EDIT: I tested several times and the first cylinder actually isn't working well either. So really none of the three is working now.
I was going to recommend lubricating the pistons, but seeing you already did exactly that, I can only say you should try to isolate the source(s) of the problem.

Since you have at least one working cylinder, the compressor and the feed tubes should be all right. This leaves the following possible points of failure: switches, subsystem hoses, working cylinders. Try disconnecting the hoses from the switches to see if the valves work well, and try connecting the compressor directly to the hoses the valves control to check the individual pneumatic circuits.

If a hose has developed a leak, you can also find it using a long hose (to protect the electronics) that is known to be leakproof and a bowl of water.

If the pistons are proven to be stuck, you can try the steps outlined in this answer.