Oil your bore?
Depends on who you talk to.
I have never oiled any of the bores in any of my clarinets. None of them has ever cracked
Some clarinet makers tell you to oil. Just as many don't.
Some techs. actually immerse wood clarinets in an oil bath for several hours.
I've known people who oil the bores of their clarinets religiously. I don't know if any of them cracked, but I do know that several people wound up with gummed up, sticky bores and degraded pads.
I've seen clarinets that have been subjected to oil baths that have come out with gummy bores that killed their sound.
Scientific tests--not merely anecdotal "evidence"--have shown that bore oil, no matter what kind, does not get absorbed into blackwood; it's just too dense. But that doesn't stop "experts" from asserting that it does.
My advice about oiling the bore: Don't bother. But if you think you must, at least use only a couple drops of oil on the swab and protect your pads by putting waxed paper under the pads before you start.
Oil your keys?
Depends on who you talk to.
I don't regularly oil my keys because I don't think the wear without oil is that significant, and I don't want oil running all over the instrument if I make a mistake.
When my instruments go in for overhaul, though, I do have the tech. oil all of the rods and pivot screws with lithium grease. I don't see any point in oiling keys without taking them off because the oil just doesn't reach the main friction areas, the rods.
10-4 good buddies.