We experimentally investigated the impact dynamics of a water drop on oil-infused nanostructured surfaces using high-speed microscopy and scalable metal oxide nano surfaces. The effects of physical properties of the oil and impact velocity on complex fluid dynamics during drop impact were investigated. We show that the oil viscosity does not have significant effects on the maximal spreading radius of the water drop, while it moderately affects the retraction dynamics. The oil viscosity also determines the stability of the infused lubricant oil during the drop impact; i.e., the low viscosity oil layer is easily displaced by the impacting drop, which is manifested by a residual mark on the impact region and earlier initiation of prompt splashing. Also, because of the liquid (water)-liquid (oil) interaction on oil-infused surfaces, various instabilities are developed at the rim during impact under certain conditions, resulting in the flower-like pattern during retraction or elongated filaments during spreading. We believe that our findings will contribute to the rational design of oil-infused surfaces under drop impact conditions by illuminating the complex fluid phenomena on oil-infused surfaces during drop impact.