(A remarkable piece of news that I must have missed...)
She pushed him away and into the wall. -> away gives no information about where he came from "into the wall" implies that he was still moving when he hit the wall.
She pushed him back to the wall -> back gives the information that he came from the direction of the wall
She repelled him as far as the wall. -> This is unlikely to be idiomatic. In this sense, "to repel" = to drive away, but it has the idea of a constant force being applied to the object that is being repelled, and is usually only used to refer (i) to an invader or an attack and usually involves many people or things, or a large amount of something being repelled.