1. Heat 2 tablespoons of the oil in a Dutch oven or large saucepan over medium heat. Add the onion and half the garlic and cook, stirring occasionally, until the onion is tender, 8 to 10 minutes. Add the tomato puree and paste, sugar, half the parmesan, 1 tablespoon of the oregano, 1/2 teaspoon salt, and 1½ cups water. Simmer, partially covered, stirring occasionally, for 30 minutes.
2. Meanwhile, in a large bowl, lightly beat the egg. Add the turkey, crackers, the remaining parmesan, garlic, and oregano, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Shape the mixture into 12 meatballs (about 1½ inches each).
3. Heat the remaining 2 tablespoons of oil in a large skillet over medium-high heat and cook the meatballs, turning occasionally, until browned, 6 to 8 minutes. Add to the sauce and simmer, stirring occasionally, until the sauce thickens, 25 to 30 minutes.
4. Cook the spaghetti according to the package directions. Serve with the meatballs and sauce. Sprinkle with parmesan and oregano before serving.