Puree one fruit at a time in a food processor or blender, until it is smooth.
Strain fruit puree through a mesh strainer to remove any pulp (save pulp to make fruit ice)
You should have approximately 2 cups of each type of fruit juice.
Mix 1/2 cup of each type of fruit juice with 1/3 cup of cornstarch. Whisk well to remove all lumps and add the cornstarch mixture back to the juice.
Working with one flavor at a time - place the juice/cornstarch mixture in a small saucepan set to high heat, and add 2 tablespoons of sugar (or to taste).
Stir constantly, and bring juice to a boil. Reduce heat to low and whisk well until the juice is thickened and smooth. Transfer to a 2 cup measuring cup for easier pouring, and divide the pudding evenly between 6 glasses or serving bowls.
Let the pudding cool in the freezer for about 10 minutes and then repeat with the remaining fruit layers.
Chill in the refrigerator for at least 2 hours and serve.