Lightly grease a pyrex or ceramic baking dish large enough to hold the ingredients with olive oil.
Slice the summer squash and zucchini into 1/2-inch thick rounds
Combine corn kernels, onion, tomato, basil, oregano, salt, and pepper in a bowl.
Tightly place a layer of zucchini and squash on the bottom of the baking dish, then scoop 1/3 of the corn and her mixture on top, followed by a layer of cheese.
Continue to layer the ingredients in this order finishing with cheese as the top layer.
Bake in the middle of the preheated oven for an hour to an hour and a half or until vegetables are tender, cheese is golden, and juices are bubbly.