What causes the surface ocean currents in the northern hemisphere to deflect to the right, and the currents in the southern hemisphere to deflect to the left?

The Coriolis force is an inertial force that acts on objects that are in motion relative to a rotation reference frame. This causes moving objects to the right ( with respect to the direction of travel ) in the Northern hemisphere and to the left in the Southern hemisphere. The horizontal deflection is zero at the equator. It also causes the surface ocean currents in the Northern hemisphere to deflect to the right and the currents in the Southern hemisphere to deflect to the left.
the Coriolis force.  

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