I was recently diagnosed with Graves Disease myself. I am currently on a gluten free and dairy free diet. I am primarily eating vegetarian, but I am including some eggs. I am juicing and drinking green smoothies. I agree that it is important to eat mostly raw food. The supplements I am using include Thyrosoothe http://www.nativeremedies.com/products/thyrosoothe-natural-remedy-for-hyperth... ,Natural Vitality Calm Magnesium, DayStar Botanicals LifeForce (super food), Acerola Cherry powder, Aloe Vera, and Cod Liver Oil. I am also using Passion Flower as a natural beta blocker (to help decrease my heart rate).
I am working with a Functional Medicine doctor http://www.functionalmedicine.org/about/whatisfm/ . They specialize in helping patients with chronic disease and autoimmune disorders get to the root cause of their illness. Since Graves Disease can have some serious consequences, I personally feel more comfortable working with a doctor who can monitor my progress.
Hope this is helpful to you.