Preheat the oven to 275. Rub the pork with chiles, salt, pepper, garlic, and press in the cloves. Place in a large roasting pan, and cover with foil. Cook until the meat is falling off the bone, about 4 hours. Once cool enough to handle, pull the meat off the bone, and shred it.
Combine the cilantro and onion. Set aside to use as garnish.
About an hour before serving, mix the sliced radishes with salt and lime juice to taste. Set aside to marinate.
Blend all ingredients, seasoning with lime juice and salt to taste.
Serve carnitas with warmed corn tortillas, garnish, salted radishes, salsa, wedges of lime and queso fresco. You can also serve this with rice and beans, but come on, you still have a night's work to do.