My hair is water only, with VERY infrequent conditioner washes, so by a lot of people's standards, my hair hasn't been WASHED persay in ummmm lets see I last shampoo in june? july? over 6 months.
It might not work for everyone, and many people have a 2 month greasy transition period (I didn't really, my hair is so dry).
I do water wash my hair oh, at least once a week, and get it wet more often (I only comb my hair wet, because it tangles less that way). When I wash my hair, I massage the scalp under the water, and make sure it gets nice and clean. I also rub the natural hair oils through my hair with hands and a boar bristle brush.
also, if my hair is smelly, (I pay very close attention to this, I don't want smelly hair), I will condition only wash. This is needed only oh... every couple months.
It doesn't smell, not to me, nor others. It's also not oily. Then again, with my hair... I don't think it COULD be oily. I do oil treatments (deep oil treatments where I apply oh... a couple tbs of olive oil, enough that my hair looks soaking wet), wear it in a scarf for two days, and by the time 36 hours rolls around, my hair doesn't even look particularly shiny in a greasy way, just a healthy way.