Combine venison, sausage, bread crumbs, 1/2 cup Parmesan cheese, parsley, and egg in a large bowl; mix until evenly combined. Form mixture into fifty 1-inch meatballs.
Heat oil in a large skillet over medium-high heat. Add meatballs and cook for 4 minutes, flipping halfway, to get an even brown on all sides. Transfer with tongs to a paper towel-lined plate.
Heat oil for soup in a large soup pot. Add celery, carrot, and onion and cook until soft, about 5 minutes. Add garlic and cook until fragrant, about 1 minute more. Add broth and bring to a boil. Stir in pasta, oregano, and meatballs. Reduce heat, cover, and cook for 10 minutes.
Turn heat off and let soup sit for 5 minutes. Stir in spinach and lemon juice. Ladle into bowls, season with salt and pepper, and garnish with Parmesan cheese.