I go to the University of Maine, but I am a New Jersey resident, which means that, unless I'm taking Summer classes, I would be in New Jersey over the Summer.

So, this being a Guard question, what would be my options in terms of drilling?

Also, has anyone ever heard of a out-of-state student getting in-state tuition?

You can enlist in the Guard in whatever state you want; you just have to be able to attend drill. My TIO lives in IL and drills in MN, for example. It's not uncommon for students to drill in a different state than where they go to school. We have a lot of soldiers that go to school in WI and the Dakotas that drill in MN. They get the same benefits as if they lived/attended school in-state.

The tuition question isn't a military one unless the state says something to that effect. In MN, there is reciprocity with neighboring states, so each student pays in-state tuition, but that has nothing to do with the Guard.

Anticipating your next question--tuition benefits that are provided by the Guard, aside from federal benefits, are provided by the state in which your unit is located. If your unit is in Maine, then you'll get Maine's educational benefits. If your unit is in New Jersey, you get the educational benefits there. You can use those benefits wherever you go to school, unless otherwise stipulated.