Heat 3 tablespoons olive oil in a medium (11-inch) pot or Dutch oven, such as Le Creuset, over medium-high heat. Add the pork and saute for 5 to 10 minutes, until lightly browned on all sides. Transfer the pork and any liquid to a bowl and set aside. Heat 2 tablespoons oil in the pot, add the onions, and saute over medium heat for 5 minutes, stirring occasionally. Add the poblano and bell peppers and cook for 5 minutes, stirring occasionally. Add the garlic, chili powder, and oregano and cook for one minute. Return the pork and its juices to the pot.
Add the chicken stock and salsa verde and bring to a simmer. Stir in the hominy, black beans, corn chips, 1 tablespoon salt, and 1 1/2 teaspoons black pepper and simmer, partially covered, for 30 minutes, stirring occasionally. Add 1 teaspoon salt, depending on the saltiness of the chicken stock and the chips.
To serve, ladle the posole into large soup bowls. Garnish with a squeeze of lime and top with avocado, scallions, radishes, tortilla chips, Cheddar, and sour cream. Serve hot.