Heat the oil in a large skillet over medium heat, and brown the pork on all sides. Reserving the juices in the skillet, transfer the pork to a slow cooker.
In the skillet with the pork juices over medium heat, saute the onion and garlic about 1 minute. Transfer to the slow cooker, along with skillet juices.
Mix the tomatillos, green chile peppers and jalapeno peppers into the slow cooker. Season with oregano, salt, and pepper. Pour in water and chicken broth, or barely cover all ingredients. Cover, and cook on High for 6 to 7 hours.
Shred the cooked pork with a fork. Spoon the slow cooker mixture into bowls, and top with Monterey Jack cheese and sour cream to serve.