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Shred zucchini and half the onion; squeeze out liquid and, in a large bowl, mix with bulgur, pork, eggs, 1/4 cup oregano, and half the garlic. Season with salt and pepper and form into 2-inch meatballs (22 to 24 total).
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In a heavy pot, heat vegetable oil over medium-high. In batches, cook meatballs until browned, 5 to 7 minutes, turning occasionally. Drain on paper towels. Discard oil; wipe out pot.
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Add olive oil to pot. Chop remaining onion and add, along with remaining garlic; cook until fragrant, 2 minutes. Add tomatoes, 1/2 cup oregano, and meatballs; cook until meatballs are cooked through and tomatoes have cooked down, 15 to 20 minutes; season with salt and pepper. Transfer 10 to 12 meatballs and 1 cup sauce to an airtight container and refrigerate, up to 3 days.
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Meanwhile, in a large pot of boiling salted water, cook pasta according to package instructions. Serve with remaining meatballs, sauce, and Parmesan.
