Heat the oil in a large pot over medium-high heat. Season the pork with 1 teaspoon salt and freshly ground black pepper to taste. Working in 2 batches so that you don't overcrowd the pan, brown the meat on both sides, about 4 minutes a side. Remove the meat as you brown it and set it on a plate.
Lower the heat to medium and add the onion to the pot. Cook until softened, about 6 minutes. Add the garlic and oregano and cook for another minute. Add the pork and chicken stock and bring to a boil over medium-high heat. Lower the heat to low and simmer, covered, for 45 minutes to 1 hour, or until the pork is tender. Remove the pork from the broth and cool.
Meanwhile, place the tomatillos and chile in a small baking dish under a preheated broiler. Broil until the tomatillos and chile are blackened in spots, turn over and blacken in spots on the other side. Let them cool and remove the stems from both the tomatillos and chiles. Transfer to a blender with 1/2 cup of the liquid from the soup, and with the pumpkin seeds and cilantro. Blend until smooth.
When the pork is cool enough to handle, shred into bite-sized pieces.
Add the tomatillo-pumpkin seed mixture and the hominy to the pot and return to a gentle simmer over low heat. Cook for about 20 minutes to allow the flavors to blend. Add the pork and remaining salt into the pot and cook for 5 minutes.
Ladle into heated bowls and serve with the avocado, cilantro, onion and lime wedges.