Melt butter in a large saucepan over medium heat. Add onion and garlic; cook 5 minutes or until tender, stirring frequently. Add well-rinsed crawfish; cook 2 minutes, stirring frequently. Remove mixture from pan; cover and keep warm.
Add cheese and tomatoes to pan; cook over medium-low heat for 5 minutes or until cheese melts. Stir in crawfish mixture and chopped green onions. Serve with tortilla chips. Garnish with green onion strips, if desired.