Line cookie sheet with foil.
Using 9 inch round plate or cake pan as guide, with toothpick, trace a circle on foil on cookie sheet.
Preheat oven to 275°F.
In small bowl, with mixer at high speed, beat egg whites, cream of tartar, and salt until whites begin to mound.
Beating at high speed, add vanilla and gradually sprinkle in sugar, 2 tablespoons at a time, beating well after each addition, until sugar completely dissolves and whites stand in stiff, glossy peaks when beaters are lifted.
Spoon meringue mixture inside circle on cookie sheet.
With spoon, shape and spread meringue into a "nest" with a 1 1/2 inch high edge.
Bake meringue shell 1 hour 15 minutes.
Turn off oven and let meringue remain in oven 1 hour to dry out.
Transfer meringue with foil to wire rack; cool completely.
Meanwhile, prepare filling: Finely grate 2 teaspoons peel and squeeze 1/2 cup juice from limes.
In medium bowl, with wire whisk, mix lime juice and grated lime peel with undiluted sweetened condensed milk and yogurt until blended.
In 1 quart saucepan, evenly sprinkle gelatin over 1/4 cup cold water; let stand 1 minute to soften.
Heat over low heat, stirring frequently, about 2 to 3 minutes, until gelatin is completely dissolved (do not boil).
With wire whisk, blend gelatin into lime mixture.
Set bowl with lime mixture in larger bowl filled with ice water.
With rubber spatula, stir mixture occasionally until it begins to thicken, about 20 minutes.
Remove bowl with lime filling from bowl of ice water.
With metal spatula, carefully loosen and remove meringue from foil; discard foil.
Place meringue shell on serving plate.
Pour lime mixture into meringue shell; refrigerate at least 1 hour or until lime filling is firm enough to slice.
Garnish with strawberry halves.