Does dish oil increase or decrease friction when rubbing grit off of a dish?
As far as friction is concerned, the oil will decrease friction between the pad being used to clean and the grit.
If you are trying to remove grit that is stuck on a dish, the task is made easier if there is less friction between the surface of the dish and the grit, this enables the grit to slide off the dish with less effort from you. You would also like to increase friction between the pad that you are using to rub off the grit and the grit itself.
Oil will not help in cleaning off grit. The oil cannot enter between the grit and the surface of the dish, which would have made it easier to rub off the grit. The oil is more likely to form a layer over the grit and when you rub with your pad, the pad will slide over this layer of oil. Using oil is not going to make it easier to clean grit that is stuck to a vessel.