On the 2x4 pieces it's the 4" dimension and the type of wood that determines the strength of the desk. If you were to use a wood like oak or maple then 3/4"x4" would work. If you used pine then 2x4 would probably be a good idea. Then on the corners I would put corner blocks to beaf up the joints. Where the L meets together I would eliminate the air between the two sections. I would make that end much like the other end only putting the end cross piece flush with the end and put tee nuts in the end piece. That way just a couple of bolts through the other piece could fasten it together.