Heat oil in a large nonstick skillet over medium heat. Add onion and garlic and cook, stirring, until beginning to soften, about 3 minutes. Add zucchini, summer squash, oregano, salt and pepper and stir to combine. Reduce heat to low, cover and cook, stirring once, until the vegetables are tender-crisp, 3 to 5 minutes.
Stir in beans, tomatoes and vinegar; increase heat to medium and cook, stirring, until heated through, about 2 minutes. Remove from the heat and stir in Parmesan.