Lightly coat a nonstick skillet with cooking spray.
Place over medium heat and add the onion and two squashes. Cook, stirring occasionally, until vegetables are soft and all liquid has evaporated, about 8 to 10 minutes.
Place the vegetables in a bowl to cool slightly. Add the egg substitute, feta cheese, flour, and oregano. Stir to combine and set aside.
Place a sheet of phyllo dough on a 9-inch pie plate, allowing any excess dough to loosely drape over the sides. Lightly coat with cooking spray. Repeat, using three more phyllo sheets, spraying after each addition. Pour the prepared vegetable-egg mixture into the pie shell and smooth out surface.
Top the pie with the remaining four sheets of phyllo, spraying each layer with cooking spray before adding another sheet. Cut the phyllo 1 inch beyond the rim of the pie pan. Fold this dough over towards the center to make an edge just inside the rim.
Bake for 40 to 45 minutes, until nicely browned and puffed.