Melt butter in a large nonstick skillet over medium-high heat. Add green onions and next 6 ingredients (green onions through garlic); sauté 5 minutes or until tender. Sprinkle flour over vegetables; cook 1 minute, stirring constantly. Gradually add milk, stirring with a whisk. Cook over medium heat until thick (about 8 minutes), stirring constantly. Stir in salt and next 4 ingredients (salt through black pepper). Remove from heat; let stand 3 minutes. Add cheddar cheese and sour cream, stirring until cheese melts. Stir in crawfish.
Preheat oven to 325°.
Add water to a medium skillet to a depth of 1 inch; bring to a simmer. Dip 1 tortilla in water using tongs. Spoon 1/4 cup crawfish mixture into the center of 1 tortilla; roll tightly, and place in a 13 x 9-inch baking dish coated with cooking spray. Repeat procedure with crawfish mixture and remaining tortillas. Spread remaining crawfish mixture over tortillas; sprinkle with Monterey Jack cheese.
Cover and bake at 325° for 10 minutes or until thoroughly heated.