Heat oil in a large nonstick skillet over medium-high heat. Add mushrooms; sauté 5 minutes or until almost tender. Add onion, bell pepper, and garlic. Reduce heat to medium, and cook for 4 minutes or until bell pepper is crisp-tender, stirring frequently. Remove from heat; stir in cilantro, lime juice, salt, black pepper, and chile.
Warm tortillas according to package directions. Spoon about 1/4 cup mushroom mixture down center of each tortilla; top each tortilla with 4 teaspoons cheese and 1 tablespoon salsa. Roll up.