Heat oil in a nonstick skillet over medium-high heat. Add zucchini, mushrooms, bell pepper, onion, and garlic, and sauté vegetable mixture 6 minutes or until tender. Remove from heat. Stir in artichokes, and set aside.
Arrange Italian bread cubes in a 13 x 9-inch baking dish coated with cooking spray. Spoon zucchini mixture evenly over bread cubes, and sprinkle mixture with cheeses.
Combine egg substitute and remaining ingredients (except oregano sprigs) in a large bowl; stir with a whisk. Pour egg mixture over zucchini mixture. Cover mixture with foil; chill up to 1 day.
Preheat oven to 325°. Bake strata, covered, 1 hour or until bubbly. Garnish with oregano sprigs, if desired.