In a 10- to 12-inch nonstick frying pan over medium-high heat, stir onion in olive oil until limp, about 1 minute. Add fish and gently stir until opaque on outside, 2 to 3 minutes. Add lemon juice and 2 tablespoons oregano (2 teaspoons if using dried) and cook, gently stirring occasionally, until most of the liquid has evaporated and fish is opaque but still moist-looking in center (cut to test), 1 to 2 minutes. Gently stir in tomatoes and add salt and pepper to taste.
Lay 4 tortillas flat on a 14- by 17-inch nonstick baking sheet (if you don't have a nonstick sheet, coat a regular one lightly with cooking oil spray). Divide half the fish mixture among tortillas and spread level to within 1/2 inch of edges. Sprinkle a third of the cheese evenly over fish. Lay another tortilla on each stack and top equally with remaining fish mixture and another third of the cheese. Cover with remaining tortillas and sprinkle remaining cheese over the top.
Bake in a 400° regular or convection oven until cheese on top is beginning to brown, 10 to 12 minutes.
Meanwhile, in a small bowl, mix crema with remaining tablespoon oregano (1 teaspoon if using dried). With a wide spatula, transfer fish stacks to plates. Top equally with avocado slices and crema mixture. Garnish with lemon wedges to squeeze over stacks to taste.