engine oil isnt "waterproof" it forms an emulsion and goes all "gloopy" (technical terms!)....
there are a few gear oils that are actually stable in water, and if you really want to use an oil use some of these EP90's.
when you get water onto your air filter, from damp days, spray, rain etc it will form a gloop...

the spray cans of filter oil are fantastic, put some waste paper down, put your filter on top and spray the filter. leave it for a bit to go "tacky" (another technical term) and put the filter back in.

you really want to be removing the engine oil from that filter......