Change views mid-movie?

If you want to simulate an orthographic camera it's going to be a lot easier to arrange your set pieces on a 3D stage and then move the stage than it is going to be to move the camera. You do that by parenting all of the set pieces (layers) to a 3D null at comp center (half the comp width, half the comp height, and zero). Then create a new camera with NO depth of field and an angle of view of about 10º will get you fairly close, but it is still not orthographic. At 10º angle of view, you will start running into some fairly serious intersection edge problems. as seen here:

The only important properties not shown are the X and Y rotation values of the cube side layers. The sides are created by rotating two of the layers on the Y axis, one by 90º and the other by 270º. The other sides are moved into position by rotating them on the x-axis in increments of 90º to complete the cube. Because the layers are 1000 X 1000 pixels and the Z anchor point is offset by precisely 500 the edges are perfectly aligned on the pixel grid. That's the easiest way as I know to create a perfect cube from solid layers in AE.

If you create your Cubes in C4D lite and use Cineware you won't end up with the edge problem and can get away with a camera angle of view at 1º.  With an angle of view that small and the camera that far away from comp center it is much easier to animate the stage than it is the camera and you will be dealing with numbers that are easier to manage.

It still won't be true ortho, like the Front view in the sample, but it will be close.

If you want to do this the easy way just go to Blender.org, download a copy of blender and choose an orthographic camera. Spend an hour or so learning how to build 3D models in Blender and texture them, then animate your move there. It will be a lot easier in the long run.