In a Dutch oven, heat oil over medium-high heat. Add onion and cook until softened, about 8 to 10 minutes. Stir in pork, and cook for 15 minutes. Add salt to taste. Garnish with radishes, tortilla strips, lime wedges, and cilantro, if desired.
Add garlic, and cook for 1 minute. Add chili powder, paprika, cumin, cayenne pepper, and oregano. Allow to heat through in oil and mix. Add in a pinch or two of salt.
Add canned chiles, tomatoes, and hominy. Sprinkle a few pinches of salt. Stir and make sure everything is well mixed. Then add in broth. Bring to a boil and then reduce to simmer for about 30 minutes. Stir occasionally.
Stir in pork, and cook for 15 minutes. Add salt to taste.
In a small bowl, mix together the radishes, avocado, lime juice, and cilantro. Give a few pinches of salt and stir together. Garnish the soup with a spoonful of radish avocado mix and broken tortilla chips.