In the shop i work in i continously come in contact with solvent cleaning dies for pm work, coolant while running grinders and mills, oils from tapping etc, so at the end of the day i really give my micrometers, calipers etc a good wipe down to remove any dirt oils etc. I do not oil any of my tools, i have all starrett stuff so i have bajillions of dollars in tools, id like to keep them working for the entirety of my career, what is everybody doing for oiling they're tools? what type of oil? I currently just wipe mine off with a microfiber towel and nothing else.
Way lube? I would not use any aerosol oil or lube, especially not WD-40. I never had a problem with tools and corrosion. Usually there is enough way lube and other oil flying around a shop to coat everything. I would be careful when wiping dust off my tools to not wipe all of that oil off of them.
I blow mine off with the air gun, gets little pieces of metal out of the teeth, and anything hidden up inside. I check them for adjustment and put a drop of Royal Purple Max Film on each contact surface and work back and forth, then towel off and put in the drawer. It's like a new caliper everyday.
I have the max film in a syringe with a needle, I use it for a lot of things and you waste less of it doing it this way.