The Mighty Avengers recently hooked up with an international paranormal investigation network called GRAMPA (don't ask) which has given them international authority to investigate and do superhero works outside the United States. The new Mighty team, consisting of Hank Pym, Jocasta, Hercules, Amadeus Cho, Stature, Vision Jr., Quicksilver, and U.S. Agent, see themselves as a global response team. They presumably get funding from either GRAMPA or the assets of Pym or even Hercules.
The New Avengers are still considered "outlaws". They haven't teamed with the Mighty team yet, but at some point they will. Why they haven't pooled resources is a good question. My answer is that the New Avengers see themselves as operating in the United States in general and New York in particular. Beyond a fight with the Fantastic Four, the Mighty Avengers have usually adventured in other countries. Norman Osborn is peeved that the international community sees Pym's team as "the real Avengers" right now.
The Dark Avengers are Osborn's flunky squad of Avengers, and most of them are psychopaths or sociopaths. He also has drafted a Dark X-Men.
