Honing Fluid/Knife Sharpening Oil
I regularly use 3-in-1 on my oilstones, to no ill effect.  A commercial honing oil is thinner, but as long as it can float the metal particles, you're good.  You can clean some out with a spray of WD-40, if it's starting to fill up.

(The knife aficionados are going to hate this answer.  It's got 3-in-1 and WD-40 in the same paragraph.)