First of all, you should use the magic cake strips to bake a sheet cake that is about 1.5 inches deep. That will start you with a nice flat top on the cake. Don't make the cake any deeper than 2", it's a lot harder to cut squares.
If you like:Cut this cake in half and fill it with icing or jam. Trim the baked edges off or not.
Stick the cake on a piece of cardboard into the fridge for an hour. In the meantime, wash a ruler (plastic or steel) to have it ready to lay on the cake.
Use the clean ruler and toothpicks to mark where to cut the cake sandwich, both at the top and along the bottom edge.
Then use a serrated bread knife to cut the cold cake by lining up the knife with the ruler and doing one cut at a time carefully. By lining up the knife at both top and bottom, your squares should be straight.