Airtool oil works really well.

Personally, I use Automatic Transmission Fluid (ATF) oil for after run oil.

When rebuilding engines, I usually use 3-in-1 during assembly, it's a little thicker than the ATF, so it coats well and allows things to slide together, but it can become gummy. ATF doesn't gum up, and protects against rust rather well.

Lots of good options out there, but automotive engine oil is a bit too thick, I think. (I also think it will burn off at a lower temp, and make a mess when it does, but I haven't tried it, so I'm guessing on that count)