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, jalapeno peppers, and cilantro into the slow cooker. Season with oregano, salt, and pepper. Pour in 1 quart water, or enough to 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, sour cream, and fresh cilantro sprigs to serve.