Sprinkle pork with salt and pepper. Warm oil in a large skillet over medium-high heat. Cook pork, in batches if necessary, browning on all sides, about 10 to 15 minutes. Add to slow cooker and drain off all but 1 Tbsp. fat. Add onion, chili powder and garlic to skillet and cook, stirring, until softened, 2 minutes. Stir in beer and cook for 1 minute, scraping up browned bits from bottom of pan with a wooden spoon. Add mixture to slow cooker
Add tomatoes to slow cooker. Cover and cook on low until meat is just tender, about 6 hours. Stir in hominy and oregano and cook 1 hour more. Remove pork from pot with tongs. When cool enough to handle, shred pork. Skim fat from top of broth, stir in shredded pork, and serve.