Oil reduces friction because a. Molecules are always moving, oil slows down that motion. Slower moving molecules get out of each others way more easily. Oil keeps moving surfaces separate from each other. Friction produces heat. Oil provides a route for heat to escape.
Lower temperatures means less binding of the surfaces.
Oil disolves molecules at the surfaces of materials so they flow out of each others way. Pressure at the knife's cutting edge causes heating of the material. The heat causes the material to loose strength and separate. The motion of the molecules in the knife's edge is what actually does the cutting. The force applied by the knife is concentrated to a small area along the knife's edge.