Question: Ignoring the whole movie situation along with the power demands, what do you think Iron Man's repulsors use to "repulse" his targets? I don't think they are lasers or electric beams, or "reverse magnetism", but I'm guessing its some sort of focused sonic waave or a shock wave generator.

Answer: 
I bet it's imagination. In imagination-land everything is possible :-)

In reality them most compact & efficient are conventional weapons.
Then probably only 10kW CO2 laser, which is real, but not as cool as in movie.
As pointed out by BarsMonster ,newton's Third law says the iron man will be acted upon by the equal and opposite force which he is exerting on any body. Hence its just mere imagination.