Melt butter or heat olive oil in a large, heavy pot. Stir in onion, garlic and jalapeño, and cook over moderately high heat until lightly browned, for about 6 to 7 minutes. Stir in corn and cook until the corn is lightly browned, about 5 minutes. Add broth, chili powder and simmer until corn is tender, about 15 minutes. Lightly season with kosher salt and pepper to taste.
Transfer half of the soup into a blender or food processor, and puree until almost smooth. Add the blended soup back into the unblended soup, and stir to combine.
Add the lime juice and zest, crabmeat and cilantro to the soup and bring to a boil. Serve hot and garnish with tortilla strips.