Preheat the oven to 375°F (190°C) and lightly grease a 9x9-inch baking dish.
In a large mixing bowl, combine the rhubarb, strawberries, granulated sugar, cornstarch, lemon juice, and vanilla extract; toss until the fruit is evenly coated.
Transfer the fruit mixture into the prepared baking dish, spreading it into an even layer.
In a separate medium bowl, whisk together the rolled oats, flour, brown sugar, cinnamon, and salt.
Integrate the chilled butter cubes into the dry mixture using a pastry cutter or fork until the mixture forms pea-sized crumbs.
Distribute the crumble topping evenly over the fruit layer in the baking dish.
Bake for 40 to 45 minutes, or until the fruit juices are bubbling and the topping is golden brown.
Remove from the oven and allow to rest for 15 to 20 minutes to allow the filling to set before serving.