Place the grapefruit juice, orange juice, water, lemon juice, and sugar in a saucepan over medium heat, and bring to a boil. Cook, stirring, until the sugar has dissolved, about 5 minutes. Remove from heat, and chill the mixture in the freezer until very cold, about 10 minutes.
Mix the vanilla yogurt with the strawberries, and chill.
Spoon a little of the cold juice mixture into 6 ice pop molds, using about 1 1/2 tablespoon of mixture for each mold. Place the molds into the freezer until the juice freezes, 30 minutes to 1 hour. Spoon about 1 tablespoon of the cold strawberry yogurt into each ice pop, and top each pop with the remaining citrus juice mixture. Freeze until fully hardened, 1 to 1 1/2 hours.