Bring 1 1/2 cups water and sugar to a boil. Cook just until clear, 2 to 3 minutes. Let syrup cool very briefly, then add 1/4 cup thinly sliced fresh basil leaves. Set aside to steep and cool.
Rinse and hull strawberries and cut them into quarters (or sixths if very large).
With a small, sharp knife, cut ends off oranges. Set 1 orange cut side down on a cutting board. Following its curve with the knife, slice off peel and white pith. Holding orange over a bowl to catch juice, cut between inner membranes and fruit to release segments; drop segments into bowl. Squeeze juice from membranes into bowl and discard membranes. Repeat with remaining oranges.
Add strawberries to oranges and pour basil syrup over fruit. Refrigerate at least 30 minutes before serving.