There is no way to bind the movement directions to the WASD or other key configurations on the keyboard. Per
How can I avoid clicking quite so much?
it appears as if you can map the key "move" command to a key and then when you place your mouse in a certain part of the screen it will allow you to use the mapped key to move to said location. That said, as far as i've found, there is no way to remove the necessity of the mouse. Keep in mind that your primary and secondary skills are also mapped to the left and right click anyway. I see your logic in wanting to be able to strafe and fire, but that would also require being able to look in a different direction than you're moving to shoot at the things behind you, which also isn't a feature in the game.