Preheat the oven to 400 degrees. Cut the spaghetti squash in half lengthwise and scoop out the seeds. Place the halves cut side down on a baking sheet and bake for 35 to 40 minutes until the flesh is tender.
While the squash bakes, heat the olive oil in a large skillet over medium heat. Add the chopped onion and cook for 4 minutes until it softens.
Add the minced garlic and ground turkey to the skillet. Cook for 6 to 8 minutes, breaking up the turkey with a spoon until it is no longer pink.
Stir in the crushed tomatoes, oregano, salt, and black pepper. Lower the heat and let the sauce simmer for 15 minutes, stirring occasionally.
Remove the squash from the oven and let it cool slightly. Use a fork to scrape the flesh into strands and divide them among four plates.
Spoon the turkey sauce over the squash and sprinkle each serving with the grated Parmesan cheese.