Oscillation refers to a periodic fluctuation of a variable, or a variation above and below a mean value, e.g. a pendulum, a periodic flow, etc, and so oscillation applies generically.
To oscillate means to swing backward and forward like a pendulum or swing, or move or travel back and forth between two points, such as a maximum and minimum.
Vibration generally refer to a mechanical oscillation, i.e. "a periodic motion of the particles of an elastic body or medium in alternately opposite directions from the position of equilibrium when that equilibrium has been disturbed (as when a stretched cord produces musical tones or molecules in the air transmit sounds to the ear)." Ref: Merriam Webster Dictionary