Preheat oven to broil with rack positioned about 6 inches from heat source. Line a large rimmed baking sheet with aluminum foil.
Arrange tomatillos, poblanos, onion, garlic, and jalapeño evenly on prepared baking sheet. Drizzle with oil, and broil until blistered and slightly softened, 12 to 14 minutes, turning once halfway through cooking. Transfer poblanos to a large heat-proof bowl; cover with plastic wrap, and let stand 10 minutes. Carefully peel poblanos, discarding skins and seeds.
Transfer tomatillos, onion, garlic, and jalapeño, along with any accumulated juices, to a blender; add cilantro and peeled poblanos. Secure lid on blender, and remove center piece to allow steam to escape. Place a clean towel over opening, and process until smooth, about 1 minute; set aside.
Place pork in a 6-quart slow cooker. Sprinkle with oregano, cumin, salt, and ground cloves; stir to coat. Pour 3 cups reserved tomatillo mixture over pork, stirring to combine; cover remaining 1 cup tomatillo mixture and refrigerate until ready to use.
Cover slow cooker, and cook on HIGH until pork is very tender, 5 to 6 hours.
Skim and discard any fat from surface, then stir in reserved tomatillo mixture; season with additional salt to taste. Serve with avocados, lime wedges, radishes, and rice. Garnish with cilantro leaves.
