Peel and section oranges over a bowl, and squeeze membranes to extract juice. Set the sections aside, and reserve 1/4 cup juice. Discard membranes. Chop the orange sections.
Combine sugar and cornstarch in a 1-quart glass measure. Stir in the reserved orange juice, 1/4 cup fresh orange juice, and lemon juice, and stir with a whisk until well-blended. Stir in the chopped oranges. Microwave mixture at high 2 minutes and 45 seconds or until thick, stirring after 2 minutes. Stir in strawberries and extracts. Serve over ice cream. Garnish with mint, if desired.