In a medium saucepan combine sugar, water, and peels. Bring to boiling; reduce heat. Simmer, uncovered, 5 minutes. Cool slightly. Strain and discard peels. Stir in orange, lemon, and lime juices.
In a blender container or food processor bowl combine half of the juice mixture and half of the strawberries. Cover and blend or process with several on/off turns or until nearly smooth (leave some small chunks of strawberries). Transfer to a 2-quart freezer container. Repeat with remaining juice mixture and strawberries. Cover and freeze 6 hours or overnight, stirring once after freezing for 3 hours.
To serve, scrape across frozen mixture with a large spoon and place into individual serving dishes (if mixture is too firm, let stand at room temperature 20 to 30 minutes). Makes 8 servings.