Remove and discard skin and outer fat from cooked pork roast. Cut meat into 3/4-inch cubes. (You should have about 4 cups cubed pork.)
Place pork in a single layer in glass baking dish. Sprinkle with chili powder, garlic, cumin, salt and black pepper. Toss pork until evenly coated with seasonings. Drizzle with lime juice and 1 tablespoon oil; toss until evenly coated. Cover baking dish with plastic wrap and marinate pork in refrigerator for 30 minutes.
Meanwhile, heat remaining 2 tablespoons oil over medium heat in 6-quart soup pot or Dutch oven. Add celery, onion, carrot, and poblano and jalapeño chiles. Cook about 5 minutes or until onion is translucent and vegetables are crisp-tender, stirring occasionally.**
Add marinated pork mixture to vegetables in soup pot. Cook for 2 minutes over medium heat, stirring occasionally. Stir in chicken stock, beer, oregano and bay leaves. Bring mixture to boil. Reduce heat to medium-low. Gently simmer, covered, for 30 minutes.
Stir together flour and 1/3 cup cold water in small bowl until smooth. Slowly stir flour mixture into stew mixture. Increase heat to medium; cook and stir for 1 minute. Remove from heat.
Serve stew in bowls or, if desired, over rice.
**Because the oils from hot chile peppers can burn your skin and eyes, wear gloves over your hands so your skin doesn’t come in contact with the oils. Also be sure to wash your hands and nails thoroughly in hot, soapy water after handling chile peppers.