Soak the different colors of hominy in separate bowls of water overnight.
In a small, dry skillet over high heat, roast the cumin and coriander seeds until they toast, about 2 minutes. When cool, grind in a food mill, mortar and pestle or clean coffee grinder.
Strain the hominy and put each color variety in its own pot, generously covering with water. Add 1-ounce of the baking soda to each pot, bring to a boil, reduce heat and simmer for about 2 hours. Add more water as needed. Check hominy for tenderness; it does not have to be completely cooked as it will be cooked further in the stew. Strain and rinse the hominy.
While the hominy is cooking, soak the dried chiles in hot water. When softened, remove the seeds and stems, then dice.
In a separate stockpot, heat the olive oil and saute the onions and garlic with the salt, black pepper, oregano, cumin and coriander until the onions are translucent. Add the diced tomatoes, tomatillos, chiles, vegetable stock and cooked hominy. Bring to a boil, then reduce heat to a simmer for about 1 1/2 hours. The posole is done when the hominy is cooked through. Add the lime juice, cilantro, and season with salt and pepper, to taste.
Posole is also delicious for breakfast, served over cornbread with a poached egg on top.
Cook's Note: You may use a combination of different kinds/colors of hominy and cook them together in 1 pot. However, the different colors will cook in slightly different times resulting in different consistencies. The blue or red hominy will break down more during cooking than the yellow or white kind. Posole, like many stews, improves with age, so cook ahead of time and reheat. It also freezes well.
Cook's Note: Native corns are available online and at most Latino markets.