In a 10- to 12-inch frying pan over high heat, tilt and shake 2/3 cup sugar often until it liquefies and turns amber, 3 to 5 minutes. At once, pour into a 10-inch pie pan (at least 6-cup capacity). Quickly tilt pan to spread syrup over bottom; it doesn't need to cover completely.
Rinse orange and lemon; with a vegetable peeler, pare off colored parts of orange and lemon peel in thin strips. In unwashed frying pan, mix peel and remaining 1 cup sugar, pressing peel with a wooden spoon to release oils.
Add milk and cream to citrus-sugar mixture. Set over medium-high heat and stir occasionally until steaming (do not boil). Cover pan and remove from heat; let stand 10 to 15 minutes.
Meanwhile, in a bowl, beat egg yolks and port to blend. Pour hot milk mixture through a fine strainer into a 1-quart glass measure; discard peel. Gradually whisk milk mixture into egg yolk mixture until blended.
Set caramel-lined pie pan in a slightly larger baking pan about 2 inches deep. Pour custard mixture over caramel. Carefully transfer both pans to a 350° regular or convection oven. Pour about 1 inch boiling water into outer pan.
Bake until center of custard barely jiggles when pie pan is gently shaken, 40 to 45 minutes. Lift custard from hot water and chill until cold, about 1 1/2 hours; cover and chill at least 12 hours or up to 2 days.
Run a knife between flan and pan edge. Invert a large rimmed platter over flan; holding pan and platter tightly together, invert and let flan and syrup slip out. Lift off pan.
Cut flan into wedges and use a pie server to transfer to plates. Spoon syrup equally over portions; garnish with sliced strawberries, if desired.