How long do you intend to age it total? 2 mo 3 mo 4mo 6mo 12 mo 24 mo? That will have an effect on how long you wash it, and how you wash it. If you are going to age it 6 months or more, I would recommend you keep it washed at least once a week for 3 or 4 of those months, you need to really build a strong, healthy rind for long term cheeses if you're going for the all natural rind, no vacuum sealing or wax or other such nonsense. And it certainly doesn't hurt to do a maintenance washing now and then either.
If you are going for a 3 or 4 mo cheese (much too short for an Emmentaler, in my opinion. But I've been spoiled I know) then I'd still say to keep it clean for at least 2 months, maybe even right to the end, as long as you give it a week or so to dry off before you bring it out and show it to the world.
No oil ever, that would not be a natural rind, and Cheeses native to the Kanton of Bern tend to be natural or washed rinds almost exclusively. It has an effect on the flavor development of the cheese. Though if you are going for an American-style Swiss, I suppose you can do whatever you want. But I'd recommend no oil.