Preheat the oven to 350°F. Butter a 9" x 9" square baking pan. Cut 2 pieces of parchment paper to fit, with sides overlapping about 2 inches. Place the first piece in pan and butter, then place the second piece covering opposite sides in pan and butter. Using metal binder clips, clip parchment to the pan. Set aside.
For the crust/ crumb topping: In a medium bowl, whisk together flour, baking soda, and salt.
Add-in both sugars and oats. Use the whisk to break up any clumps of sugar. Stir to combine.
Whisk vanilla and butter together and add to the oat mixture. Stir with a rubber spatula or wooden spoon to combine, making sure it's evenly moistened.
Scoop out 1/3 of the crumb mixture and set aside. Press the remaining crumb mixture into the bottom of the prepared pan. Set aside while you prepare the filling.
In a small mixing bowl combine sugar and cornstarch.
For the filling: Combine strawberries and rhubarb in a mixing bowl and toss with lemon juice.
Pour cornstarch mixture over strawberries and rhubarb and toss to coat.
Spoon strawberry mixture over crust in the pan in an even layer. Sprinkle the remaining crumbs over the top evenly.
Bake in preheated oven for 45 - 50 minutes until filling is bubbly and the top is golden brown.
Cool in the pan on a wire rack until warm. Grabbing the sides of the parchment, remove from pan, and slice while warm or cool completely.