Place wheat berries in a small stockpot over high heat. Add the water. Cover; bring to a boil. Reduce heat to low. Simmer until tender, at least 40 minutes. Drain; set aside.
Fill a large bowl with ice and water; set aside. Bring a medium pot of water to a boil. Add the broccoli, and blanch until bright green, 1 to 2 minutes. Transfer to the ice bath, and set aside.
Heat the olive oil in a large skillet over medium-low heat. Add the onion and garlic, and cook, stirring frequently, until translucent, about 10 minutes. Raise heat to medium, and add the tomatoes, oregano, zucchini, eggplant, salt, and pepper; cook, stirring occasionally, until the vegetables have softened, about 15 minutes. Add the broccoli and wheat berries, and continue to cook until broccoli and wheat berries are heated through, about 3 minutes more. Serve.