Are there any buildings that use up oil, or is it only troops that consume it?

Fuel is also used in the power plants to product electricity (power), but you will refill these manually as needed. The only way to reduce the regular consumption is through having less vehicle troops. Or with the hero 'the mechanic' stationed in the Vehicle factory and the right skill unlocked.

This only affects the production and warehouse storage of fuel though. If you are able to complete daily challenges and CoZ challenges regularly then you will be able to stock up on fuel storage items which you keep until needed for upgrades / research etc.