Heat the vegetable oil in a large pot over medium-high heat. Stir in the button mushrooms, oyster mushrooms, and enoki mushrooms; cook and stir until lightly browned. Add the onion, celery, green bell pepper, carrot, and garlic. Season with salt and pepper. Cook and stir for 3 to 4 minutes. Mix in the chicken broth, cream-style corn, chicken, rice wine vinegar, and five-spice powder, and bring to boil. Cover and reduce heat to medium-low. Simmer for about 20 minutes. Mix cornstarch with the milk in a small bowl, and stir into the soup. Stir until soup has thickened. Garnish each serving with chopped basil.