Water...isn't as easy to clean in my opinion.
I thought the opposite. Now granted, most of the times when I used oil I did so as a small boy with my Dad. We did have to wipe the stones down with some form of rag or towel. Sometimes he had a sealed container to store the rag, sometimes we just threw out a paper towel.
When I sharpen now, I carry several old wash clothes. Ben has sent me some very nice absorbent ones. I simply wash these out with my gym clothes every night.
As for maintnence, I flatten my stones near a sink. I just flush the swarf down the drain when I do a final thorough soak. Obviously there is no smell.
And frankly, I'm getting better edges.
I am considering getting a large fine grain oil-stone to polish off the final burr on expensive chef knives. Many people here seem to like oil for some applications.