In a blender, puree tomatillos until smooth; set aside.
In a 5-quart Dutch oven or heavy pot, heat oil over medium-high. Season pork with salt and pepper. Working in batches and transferring to a plate as you go, brown pork, 6 to 8 minutes per batch (lower heat if bottom of pot begins to darken).
Return pork (with any juices) to pot. Add tomatillos, green chiles, oregano, onion, garlic, jalapenos, and 1 cup water; season with salt and pepper, and stir. Bring to a boil; reduce to a simmer. Cover, and cook, stirring occasionally, until pork is tender, about 2 hours. (To store, refrigerate for up to 3 days, or freeze for up to 3 months.).
Just before serving, stir in chopped cilantro; serve chili with cheddar and lime wedges, and garnish with cilantro leaves.