In short: the mineral oil will float away, and the metal exposed to air and water may react violently, yielding an explosion. Do not do this.
During shipment and storage, because of sodium's density of about 0.96 g/cm$^3$, the metal will be covered by the mineral oil. This intends to keep oxygen and water away from the bare metal. If you find someone shipping it (it is banned from air planes, for example).
If take the ingots / cubes of sodium out of the mineral oil, and remove adsorbed oil for example with filter paper, the shiny surfaces quickly become dull. Oxygen and especially moisture present in the air attack the metal, mainly to form a white surface of $\ce{NaOH}$.
Bare pieces of sodium, exposed to water, will vigorously react to yield both $\ce{NaOH}$ and hydrogen gas. Because of the lower density of the metal, compared to the one of water (1.00 g/cm$³$), it will float on the later. However this said reaction is highly exothermic, and may ignite the hydrogen generated as shown here.
Disclaimer: Do not repeat this. This is nothing funny, it is highly dangerous to you (as hot shrapnels of metal may hit you, and you may expose yourself to highly concentrated lye), to others around, and to the environment. (In addition, he handled the metal without appropriate gloves, nor safety goggles, nor lab coat...). Do not throw sodium into a pond. Think first, than act responsibly.