Preheat the oven to 325°F (163°C). Lightly grease a 9-inch springform pan and line the bottom with parchment paper.
Make the crust: Combine Oreo crumbs and melted butter in a mixing bowl. Press evenly into the pan’s bottom. Bake for 10 minutes, then cool completely.
Prepare the cheesecake base: In a large bowl, beat cream cheese until smooth. Add sugar and mix until creamy. Blend in sour cream and vanilla.
Add the eggs: Beat them in one at a time, just until incorporated—overmixing can lead to cracks.
Divide and flavor: Separate the batter into three equal portions. Stir the melted semi-sweet chocolate into one, milk chocolate into the second, and white chocolate into the third.
Layer it: Pour the semi-sweet chocolate batter first, followed by milk chocolate, then white chocolate. Smooth gently after each layer.
Bake: Set the cheesecake on the middle rack. Bake for 60–70 minutes, or until the edges are set but the center still slightly jiggles.
Cool gradually: Turn off the oven, crack the door open, and let it cool inside for 1 hour. This prevents cracks.
Chill: Refrigerate for at least 4 hours—or overnight for best results.
Decorate: Top with whipped cream, chocolate curls, and fresh berries just before serving.