A pumping device includes a container having a cover structure. A piston is movably received in the container and is manually operable. The cover structure has an air inlet valve and a slide switch, which, when properly set, allow air to be sucked into or expelled out of the container by the manual operation of the piston to increase or decrease the internal pressure of the container for oil suction and oil drainage. The pumping device also includes another slide switch, whereby when both slide switches are properly set, the internal pressure of the container is increased or decreased due to the supply of pressurized air from an external source and oil can be sucked into and drained out of the container accordingly.