In a small bowl, whisk together the flour, baking powder, and salt. Set aside.
In a medium sized mixing bowl, with a hand mixer (or stand mixer fitted with the paddle attachment) beat together the softened butter and sugar for 3-4 minutes, until the mixture is light and fluffy.
Scrape down the sides of the bowl, then beat in the egg and vanilla until well combined.
Pour half of the flour mixture into the bowl, then use a rubber spatula to gently fold the ingredients together just until no flour streaks remain. Add in all of the sour cream and milk, fold, then gently fold in the rest of the dry ingredients.
Add half of the cake batter to the prepared loaf pan. Dollop the cheesecake filling over the batter and carefully spread it into an even layer over the cake batter.
Dollop the remaining cake batter over the cheesecake batter and carefully spread it into an even layer. Dollop the mixed berries over the cake batter and carefully spread those into an even layer, then top the whole thing off with the streusel.
Bake for 40-50 minutes, until a toothpick inserted in the center of the coffee cake comes out with just a few moist crumbs. Allow the cake to cool to room temperature, then slice, serve, and enjoy!