What causes the Sun to oscillate north and south of the galactic plane?

ALL the stars in a galaxy rotate around the multimillion solar mass black hole at their centers. This is conservation of angular momentum and energy. A cosmic year for the Solar System is from between 230 to 260 million years, depending on your source, The values average out to 250 million Earth years for one cosmic year for the Solar System. This is basic physics and orbital mechanics.