Bring water, sugar, and strawberry-flavored gelatin to a boil in a large saucepan; boil for 3 minutes. Stir in pineapple juice, lemon juice, and orange juice.

Divide mixture between 2 freezer-safe containers. Cover and freeze until solid, at least 8 hours.

Combine contents of 1 container frozen juice mixture with 1 bottle lemon-lime flavored carbonated beverage in a punch bowl; stir until slushy. Repeat with remaining portions as needed.