In a large deep pot, combine pork and water. Bring to a boil, skimming scum that floats on top.
When the broth clears, add onion, garlic, bay leaves, and 2 tablespoons of salt. Lower heat, cover and simmer for about 1 to 1 1/2 hours, adding more water in 1 cup increments as needed to maintain about 4 quarts.
Remove stems off chili pods. Pry open and remove seeds. In a bowl, soak in about 2 cups warm water for about 30 minutes or until softened.
In a blender, process softened chilies and the soaking liquid until smooth. Using a fine mesh sieve, strain the red sauce to remove any stray bits and pieces.
Add red sauce to the pot of simmering meat. Add Mexican oregano and cumin.
Add hominy. Continue to simmer, covered, for about 1 to 1 1/2 hours or until meat is fork tender. Season with salt to taste.
Ladle soup into bowls and garnish with toppings. Serve piping hot with tostadas and lime wedges.