Prepare a grill or grill pan for medium heat.
Put the asparagus, squash and zucchini in a large bowl and drizzle with olive oil. Season with the oregano and some salt and pepper and toss to coat. Grill, turning, until cooked through but not mushy, 5 to 8 minutes total.
Meanwhile, grate the garlic into the balsamic vinegar in a small saucepan and reduce over medium heat until syrupy, about 10 minutes. Drizzle over the veggies before serving.