Preheat oven to 200 degrees with rack in lower third. Coat two baking sheets with nonstick cooking spray; line with parchment paper.
With an electric mixer, beat egg whites with salt and cream of tartar until soft peaks form. Very gradually beat in sugar, adding 1 tablespoon at a time; beat until stiff and glossy.
Drop 8 mounds of meringue onto prepared baking sheets; twirl a teaspoon in the center of each to spread to a diameter of 4 inches and create a nest. Bake until dry but still white, about 1 1/2 hours, rotating baking sheets halfway through; let cool on sheets.
Use a small paring knife to hull and quarter strawberries. In a bowl, toss strawberries with sugar; let stand, at least 30 minutes. Spoon into nests.