In the bowl of an electric mixer fitted with a whisk attachment, combine the sweetened condensed milk and cream cheese and mix on low until smooth, 2 to 3 minutes. Add the sour cream and mix until smooth.
Put the lime gelatin in a medium heatsafe bowl, pour in 1 cup boiling water and gently stir until completely dissolved. Add the gelatin mixture to the cream cheese mixture and stir until combined. Pour the mixture through a fine-mesh strainer into a mixing bowl to remove any lumps.
Spray a 10-cup fluted bundt pan with cooking spray. Pour the lime gelatin mixture into the prepared pan. Use a spoon to push the pineapple and cherries into the mixture and distribute them throughout. Refrigerate until set, about 2 hours.
After about 1 1/2 hours, put 2 cups cold water in a medium heatsafe bowl. Add the strawberry gelatin and let bloom for 5 minutes. Add 2 cups boiling water and stir until completely dissolved. Cool to room temperature, about 30 minutes.
Dampen a baking sheet with a little water and set aside. Fill a bowl larger than the bundt pan with warm water (make sure it's not too hot). Dip the bundt pan into the water in 5-second intervals (don't hold it in there too long) to loosen the lime gelatin from the pan. This may need to be repeated a few times until you see it start to loosen from the sides and center. Once loosened, place the baking sheet on top of the bundt pan and flip to invert the lime gelatin onto the baking sheet. Lift the bundt pan off the gelatin and rotate it slightly, then place it back over the gelatin so the fluted ridges of the bundt pan and the molded gelatin do NOT line up (the strawberry gelatin layer will fill the spaces).
Flip the bundt pan and baking sheet back right-side up so the lime gelatin is back in the pan but slightly off center. Pour in the cooled strawberry gelatin mixture; the lime gelatin should float in the strawberry liquid. Using your fingers, realign the lime gelatin with the proper grooves of the pan. Refrigerate until set, about 2 hours.
Dip the bundt pan into a bowl of warm water (following the method above), being careful not to hold it in there too long. Place a serving dish on top of the bundt pan and flip to invert the gelatin ring onto the dish.
Inverting the gelatin mold onto a damp baking sheet makes it easy to slide the ring around and prevents suctioning.