In a medium bowl place the ground beef, the 2 teaspoons of oregano, the 1 clove of minced garlic, and the salt. Mix the ingredients together with your hands so that they are well combined. Roll the meat into 1" round meatballs. Preheat the oven to 400 F. Place the meatballs on a flat sheet and bake them for 8 minutes, or until they are pink in the middle. Set the meatballs aside. In a large stockpot place the olive oil and heat it on medium high until it is hot. Add the onions and zucchini, and saute them for 2 to 3 minutes, or until the onions are clear. Add the 5 cloves of diced garlic and the 1 1/2 tablespoons of oregano, and saute them for 2 minutes. Add the tomato paste and tomato sauce. Stir the ingredients together and cook the ingredients for 2 minutes. Add the water. Bring the liquid to a boil and then reduce the heat to low. Simmer the soup for 45 to 60 minutes, or until the desired consistency is achieved. Add the meatballs and the cooked rice. Add more salt if necessary.