Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius). Lightly grease a 9 x 12-inch (23 x 30 cm) baking dish.
Heat olive oil in a large frying pan over medium-high heat. Sauté diced red onions for about 5 minutes until lightly golden.
Add fresh spinach to the pan and sauté for an extra 2-3 minutes until wilted.
Stir in sliced kalamata olives and diced tomatoes into the vegetable mix.
Spread sliced pita bread in the prepared baking dish. Layer sautéed veggies over the pita, then sprinkle with crumbled feta and shredded mozzarella.
In a separate bowl, whisk together eggs, milk, dried oregano, salt, and pepper.
Pour the egg mixture evenly over the ingredients in the baking pan.
Let the mixture sit for 30 minutes to soak, or refrigerate overnight.
Bake the strata in the oven for 40-50 minutes until puffed up and golden brown.
Allow the strata to rest for 15 minutes before serving to set and cool slightly. Enjoy your delicious Greek egg bake!