Cook sugar, ginger, lime juice, and 3 tbsp. water in a medium saucepan over medium heat until sugar dissolves, 1 to 2 minutes. Remove from heat and let cool slightly, about 5 minutes.
Combine oranges and strawberries in a small bowl, then pour warm syrup over fruit.
Divide yogurt among 4 parfait glasses or bowls. Drizzle each with honey. Spoon fruit mixture over yogurt.