Preheat the oven to 350°F and line a 9x9-inch baking pan with parchment paper and set aside.
Combine graham cracker crumbs and sugar in a medium bowl and make a small well. Pour the melted butter in the well and mix until evenly combined.
Transfer the crust mixture to the prepared baking pan and gently press the mixture evenly into the bottom of the pan. Bake for 8 minutes.
While the crust is baking, beat together the cheesecake ingredients in a medium bowl until smooth and creamy and set aside.
Add the strawberries, lemon juice, and vanilla to a medium saucepan and cook over medium-high heat for 5 to 7 minutes until the strawberries are bursting and juice has started to form.
In a separate bowl, combine the brown sugar and cornstarch. Then stir it into the strawberry mixture and cook for an additional 2 minutes, stirring constantly. Once the mixture has thickened and resembles pie filling, remove from heat.
Make the oatmeal crumble by combining all of the ingredients in a large bowl and use a pastry cutter or your fingers to mix the ingredients together, squishing the cubes of butter and creating a coarse crumble.
Pour the cheesecake mixture over the baked crust and spread out evenly. Top the cheesecake mixture with the strawberry sauce. Top the strawberries with the crumble topping.
Bake the cheesecake bars for 50 to 70 minutes, until the top of the crumble is golden brown. Remove from the oven and let cool in pan on a wire rack for 30 to 60 minutes. Transfer to the refrigerator to cool for at least 4 hours, preferably overnight, before slicing into squares.