Put all of the ingredients in a glass jar and shake. Keep refrigerated until ready to use.
Bring the water to a boil in a soup pot. Add salt and wheat berries, reduce the heat to medium, cover, and cook until the wheat is tender and slightly al dente, about 1-1 ½ hours.
In a large bowl, combine the cooked wheat berries, avocado, tomatoes, and parsley. Add salad dressing to taste and carefully toss together.