Select layers 5,6,7 which are the "connect 2 to 3", "connect 3 to 4", "connect 4 to 1", and hit the "U" key to reveal the beam effect properties.
Start by twirling down the arrows for the start and end points of the "connect 2 to 3" layer to reveal the pick whip for these parameters.
Drag the pick whip "START" to the position property of "Object 2" and the "END" pick whip to the position of "Object 3", and hit the "ENTER" key on the numeric key pad.

Repeat this step of pick whipping for "connect 3 to 4" and "connect 4 to 1"
For additional movement you can now go back and key frame position for the object layers.
Have fun!