In a medium bowl, combine the diced tomato, red onion, squeezed spinach, crumbled feta, shredded mozzarella, and dried oregano. Squeeze the spinach firmly over the sink before adding to remove excess moisture. Toss gently until the filling is evenly mixed.

Lay the three tortillas flat on a clean work surface. Divide the filling evenly across one half of each tortilla, keeping it about half an inch from the edges. Fold each tortilla in half over the filling and press down gently to seal.

Heat a large skillet over medium heat and add the olive oil. Once the oil shimmers, place one or two folded quesadillas in the pan. Cook for 3 to 4 minutes per side until deep golden brown and crispy and the cheese is fully melted. Work in batches to avoid crowding.

Transfer the cooked quesadillas to a cutting board and let them rest for 1 minute. Slice each into wedges and serve immediately while warm.