Oscillation is rhythmic process of object to continue it's repeating at certain interval of time, That interval is almost constant or proportionately decreasing. Under stimulated external force with a certain magnitude and direction produce oscillation of object, with continuously decreasing repetition time interval in traveling path. 

Vibration is just a random motion of an object within limited path of movement it doesn't show any rhythm or continuous repetition or like that, So, vibration is random motion of object under external forces, in other words, doesn't follow any proportionality.