Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9x5x3-inch loaf pan.
Pour vinegar into a measuring cup. Fill with milk to the 1/2 cup measuring mark. Set aside.
Blend sugar, cream cheese, and butter together using a pastry blender in a large bowl until combined and smooth. Add 1 egg at a time, blending after each addition. Add vanilla extract and mix until combined.
Combine flour, baking powder, baking soda, and salt in a small bowl. Stir together until combined. Fold a quarter of the flour mixture at a time into egg mixture until batter is doughy. Fold in milk-vinegar mixture until blended, making sure not to overmix. Mix in mashed strawberries with their juices just until combined. Pour dough into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center of the loaf comes out clean, 50 to 60 minutes.