Sprinkle the oats in a single layer in a large shallow pan and toast them lightly over a moderate heat. Remove from the heat when they smell warm and nutty and their colour will darken slightly.
Let the oats cool, then put them in a bowl with the apple juice, honey, grated apple, a little sugar if you wish, and a generous pinch of salt. Cover and refrigerate overnight.
Slice the strawberries, put them in a mixing bowl and scatter the sugar over them. Squeeze in the orange juice, then add a few drops of balsamic vinegar to taste. Set aside in the fridge overnight.
Next morning, fold the yogurt into the bircher muesli followed by the strawberries, then serve.