To make the pico de gallo, combine the tomatoes, onion, jalapeños, cilantro, lime juice, and oil together in a medium bowl. Season with salt and pepper.
For the filling, heat the oil in a large skillet over medium-high heat. Add the turkey and the chili power, cumin, garlic powder, onion powder, paprika, oregano, and salt. Cook, stirring often, breaking up the turkey with the side of a spoon, until the turkey begins to brown, about 5 minutes. Stir in the water and reduce the heat to medium-low. Cover and simmer until the turkey is cooked through, about 5 minutes.
Preheat the oven to 400°F. Line 2 large baking sheets with aluminum foil.
Spread the tortilla wedges on the baking sheets and spray with the nonstick spray. Bake until golden brown and crispy, about 5 minutes. Remove from the oven.
Spray a large, shallow baking dish with nonstick spray. Spread half of the tortilla wedges in the baking dish, and top with half of the cheese, half of the turkey mixture, half of the beans, and half of the olives. Top with remaining tortilla wedges, and repeat with the remaining cheese, turkey mixture, beans, and olives. Bake until the cheese melts, about 10 minutes.
Remove from oven and sprinkle with half of the pico de gallo and the avocado. Spoon a large dollop of the sour cream on top of the nachos. Sprinkle with the scallions. Serve immediately, with the remaining pico de gallo on the side.