How is the National Guard Funded? Are they primarily funded by state governments or the national government? If this is true, then does the national guard divisions in each state constitute the "state militias" As privided for by many state constitutions?

I'm not sure how the responsibilities are divided, but it appears that the National Guard receives both federal and state funding. Here's an article on federal funding:

http://www.nationaldefensemagazine.org/article.cfm?Id=386

I've also seen outlays in state budgets. It appears that the federal government is paying for weapons (tanks, planes, etc.) and the state is paying for buildings and their maintenance, possibly training as well.

Each state has it's own national guard, and the governor has the authority to call on them for service. (The federal government retains the right to call on the national guard in national emergencies or to participate in military activity in the same way that the US Coast Guard is part of the US Navy in times of war.)

Yes the National Guard receives both Federal and State funds. How much they get from the Federal side depends on how well their respective representatives lobby for the types of units and equipment that each state will have. For example, a state that has an Apache Helicopter Battalion will receive more funds than say one that only has a light Infantry Battalion and so on. The National Guard is considered as part of the "total force" and each state does have to pony up enough funds to ensure that their units meet the federal standard. Hope that is clear enough.