Remove stems, seeds, and internal membranes of all peppers, and rinse.
Combine peppers, onion, garlic, and cilantro in a food processor. Pulse until finely chopped. Add tomatillos, avocado, lime juice, and salt; process until smooth. Pour in chicken broth in a slow thin stream while continuing to process.
In a large saucepan, heat the olive oil over medium heat. Add the mixture in the food processor all at once. Bring to a boil, then reduce to a simmer. Cook for 15 minutes.
Blend the crabmeat and sour cream together.
Spread some of the tomatillo sauce on a tortilla. Spoon about 2 Tbs. of the crabmeat filling across the middle of it, then roll it up. Place the tortilla seam side down in a shallow casserole or baking dish. Repeat until all tortillas are filled.
Pour tomatillo sauce over enchiladas, making sure the sauce leaks from the ends. Sprinkle cheese over all and bake in a 350-degree oven for about 15 minutes--until cheese melts and begins to bubble. Serve hot with sour cream and guacamole.