Every once in a while I go through this week long stage where my hands shake badly and my body will randomly twitch all over, what in the world!?

Shaking and twitchin. There are a number of possible causes for your symptoms. I would recommend that you see your primary care doctor for an evaluation and examination.
Shakes. Although, it is very hard and even impossible to make diagnosis based on your description, one common thing that is encountered in practice is hypoglycemia (blood sugar bottoming). It may be true in instances when one has been starving for a while, whereas in rare case one may have a tumor that secretes excessive amounts of Insulin that causes sugar drops. I recommend you see a doc.