I once had a job operating screw machines ... think of an early form of automated lathe. These machines - which had their heyday in the 50's - always managed to have a fine mist of oil about them; as a result, since then, I've kept my hair real short.
Now, for your problem .... the greases used are developed to be exceptionally water resistant. Pre-cleaning the area (steam hose), then getting into a boiler suit seems the only way to reduce the mess.
Otherwise, various towels and rags are sold specifically to catch / absorb oils. These can be used to blot the grease away, as the grease seems to prefer the fiber to you. Even ordinary toilet paper - even the shiny foreign kind - seems to do this quite well.
My last thought ... have you tried baby oil? That stuff seems to work where most else fails.
