1. Preheat oven to 350°. Wipe chiles clean with a damp cloth. In a dry, heavy saucepan over medium heat, toast chiles until fragrant and puffy, turning occasionally to keep them from burning, 3 to 5 minutes. Let cool slightly, then remove stems, seeds, and membranes. Pour beer and tequila over chiles to soften.
2. Meanwhile, season pork with salt. Heat oil in a heavy, large ovenproof pot such as a Dutch oven over medium-high heat. Brown half the pork at a time, turning as needed, 8 to 10 minutes per batch. Transfer browned pork to a bowl.
3. Add onion and garlic to pot; cook until soft, stirring often, 5 minutes. Stir in beer mixture, tomatoes, oregano, cumin, and pork. Add water if needed to barely cover pork. Bring to a boil over high heat; cover.
4. Bake stew until pork is falling-apart tender, 3 hours. Skim fat. Ladle stew into bowls and serve with accompaniments.
*Find in the Latino foods aisle or spice aisle of a supermarket, or at a Latino market.
Make ahead: Chill, covered, up to 2 days.
Note: Nutritional analysis is per serving.