Do the Transformers ever need maintenance like a normal car? Do they need to regularly oil themselves, change tires, refill on oil, etc.?
They certainly need maintenance of some kind. While we don't know the details, there are a few specific things we know or can guess:
Transformers need to refuel on some regular or semi-regular basis; energon is clearly an extremely energy-dense material but they still need to go through a lot of it. (In the G1 comics, earthbound Transformers were able to substitute petroleum fuels, but only after a lot of chemical experimentation, and they needed a lot of it.)
Early in the G1 comics (US issue 15), Hoist is seen performing "routine check-ups" for all of the Autobots in the Ark, so clearly there are routine maintenance tasks which don't require Ratchet's level of skill but must be performed. (Skids comments to a complaining Tracks: "You know the rules - every 1200 miles or four Earth weeks".)
We've seen Transformers blow a tire due to damage, so clearly they can need to replace tires. (It's possible that this is a result of adapting Earth-like alt modes, and did not happen to the original Cybertronian forms.)
During the brief period in which an injured Skids deserts the Autobots, he is driven by a human. it is clear that his reluctance to return is in part based on how much he's enjoying the regular washing, polishing and oil changes. If not actually necessary, those are certainly desirable.
The Transformers (at least in the comics and the animated shows) do show signs of wear and tear through time, and are subject to a myriad collection of diseases that target their unique biology (technology?). Ailments include the more common regular rust and sticky joints, to serious diseases like cosmic rust. Here's this conversation after Kup gets fixed by Hot Rod in Transformers: The Movie (1986):
Kup: Anyway, all things considered you did an amazing job, lad. Amazing!
Hot Rod: Really?
Kup: Yeah. You even got rid of a nasty burr in my rotator.
Transformers go through a whole range of treatments, from simple ones like lubrication and paint jobs, to more serious ones like major parts replacement and body swaps. That's why the Transformers have a whole sub class of medics that treat these problems, the most famous of them being Ratchett.
Everything and every being that exists in universe need maintenance. The biggest of the stars and galaxies die out eventually. Even the non physical things like "relationships" need maintenance.
Practically speaking, only the type and the duration of maintenance may differ for each of the living/non living things. So for transformers, may be they oil themselves say after 50 years with a some special type of oil and they may change or regenerate their tires according to its technology. But in the end they need to maintain themselves to survive..