I am on an iMac. Looking horizontally, W, S gives forward, backward (into the screen and out); A, D gives left, right; and E, Q give up, down, all as expected.
If I tilt the camera straight down, W, S give down, up, and A, D gives left, right as I would expect. However, I would expect E, Q to now give forward, backward (into the screen and out). However they give up, down not forward, backward. So there is no way to move in and out of the screen.