How can a photon oscillate when it experiences no time? How can light experience change if it is motionless in time? 
 A: Light is composed out of zillions of photons. The ensemble does have a distribution in time dependent on how the photons combine to give the classical electromagnetic field.
A photon  (in your title) is an elementary particle that moves on the geodesic with velocity c. It does not oscillate, it is the probability of finding it at (x,y,z,t) that has a sinusoidal distribution. Its only experiences are interactions with  other elementary particles. It only has energy, momentum and spin, no oscilations describe it.
This is an experiment with single photons at a time,

From left to right photons accumulate, and the last frame is the probability distribution for finding the photon at (x,y,z) which shows a wave nature. The point footprints of the photon do not oscillate.
Alternatively a photon can be described as an excitation of the photon field which excitation moves along the geodesic with creation and annihilation operators on the photon vacuum state. Motion implies time.

"motionless in time"

is a concept that comes from misunderstanding the use of limits  and ignoring that the photon is massless. This almost duplicate question's answers may be useful for you.
No mass can reach the velocity of light because it will become "infinite" and infinite energy would be needed for its existence. Only zero mass particles can move with the velocity of light. Velocity means dx/dt  , a space and a time coordinate, space measured by a meter and time by a clock plus a specific reference frame where the meter and clock are . A massive system with a clock on it, depending on the relative motion of the observer, will be running slower in ticking the seconds than the clock on the observer's frame. A photon from any observer reference system will be moving with velocity c with respect to that observer, and every other one,  even if he/she approaches the speed of light. But the observer being massive will never hit the speed of light. That is what the special relativity equations dictate and have been found to correctly describe what nature does.
A: The electric field at a point A changes based on the electric current at A and the spatial variation of the magnetic field at A.
The magnetic field at A changes based on the magnetic current at A (which is zero, since there are no magnetic charges) and the spatial variation of the electric field at A.
So that's what happens. At every point in space there is an electromagnetic field. And a current. And the two together each has a value at every point. And those values tell the field how to change.
So the field values right there change in time. The fields don't move from here to there.
Sure, for some solutions the fields here and now might look very similar to the fields that were over there a moment ago. But that's not what happened. What happened is the fields right here changed based on what was going on right here.
Now energy and momentum flows. But that's different. And momentum flows because of stress, and the stress is a real thing, as real as the electric current. And just like current flows becasue of the charge and it's velocity to give a flux of charge. There is a flux of momentum and it's called stress. The flux of energy exists too.
But if either has a velocity that's just the velocity it has. Unlike charge, it isn't a thing that flows around according to its own clock. It is completely fixed by the fields, and the fields don't move, the value at each place changes in time.
