Remove the zest from the oranges with a vegetable peeler, being careful to avoid the white pith. Put the zest in the bowl of a food processor fitted with a steel blade. Add the sugar and pulse until the zest is very finely minced.
Cream the butter in the bowl of an electric mixer fitted with a paddle attachment. Add the sugar/orange zest mixture and mix until light and fluffy. Add the eggs, one at a time, then add the orange juice and salt. Mix until combined.
Pour the mixture into a 2-quart saucepan and cook over low heat until thickened, about 10 minutes, stirring constantly. The orange curd will be ready when it coats a spoon, and it will register about 175 degrees F on a candy thermometer. Be careful not to overcook, or it will curdle. Remove from the heat and let cool or refrigerate.
Place the orange curd in a bowl and decoratively arrange the strawberries on a serving platter around the bowl.