Lets properly define what we need because I think we have a word salad here. We have electric fields and magnetic fields, both are created and changed by charges. For magnetic fields it would be moving charges, so you can be neutral and still feel its effects, and the electric field is for all charges, stationary or moving.
Electrons create an electric field, on their own, this field is unchanging. When they move around however, the field has to change as well, and in the process also create a magnetic field (only a little fib, again we don't need QM to explain EM waves), so now even neutral bodies carrying currents can be affected by it. If you moved the electron back and forth and measured the field, you'd see the field oscillates with a lag.
If you put a series of sensors in a line you'd see a wave because the lag increases with distance.
You see the field is what oscillates, if the electric field oscillates, so does the magnetic field which is dependent on changing fields and moving charges.
Using maxwell equations you'd see that in free space, the wave propagates itself at the speed of light, so it will never stop until it loses energy, how? when it causes charges to move.
The oscillation IS the EM wave itself. What starts the wave is moving charges and changing fields.
Photons are the product of finding out that the wave has its energy quantized. Which means it is some amount multiplied by an integer greater than zero if a wave is present. Photons are there to be the quanta of EM waves, and charged particles will emit photons to interact with one another.