Preheat oven to 350°F. Combine rhubarb, strawberries, 2 tablespoons sugar, cornstarch, orange zest, vanilla, chopped ginger and ⅛ teaspoon salt in a large bowl. Transfer to a shallow 2-quart baking dish.
Combine oats, flour, the remaining 1 tablespoon sugar, butter, oil, ground ginger and the remaining ⅛ teaspoon salt in a medium bowl. Sprinkle the crumb mixture over the fruit.
Bake until the fruit is bubbly around the edges and the topping has browned, 30 to 35 minutes. Let cool on a wire rack for about 10 minutes before serving.
