Blend the strawberries, water and sugar in a blender until smooth. In a small bowl, whisk together lemon juice and cornstarch for 1 minute; add to the strawberry mixture and continue whisking for 30 secs. Strain the mixture into a medium saucepan. Simmer over medium heat until the mixture starts to boil. Stir frequently and cook a few more minutes or until it thickens. Strain again and let cool to room temperature.
For the crust:
Crush Oreos in a ziplock bag. Mix with the melted butter and sugar. Spoon about 1 tablespoon of the mixture into a lined cupcakes pans. Be sure to line the pan with cupcake liners or lightly grease the pans. Press gently with the button of the scooper or spoon to form even layers. This layer should occupy less than 1/4 of the cupcake molds.
For the Cheesecake
Heat oven to 350 degrees. In the large bowl, beat together cream cheese and sugar until light and fluffy. Please do not skip this step because if the cream-cheese and sugar are not creamed they will clump up with the eggs. Reduce speed to low and beat in eggs, one at a time until they are fully blended in. Beat in sour cream and vanilla until well combined.
Pour the batter into the cupcakes molds until they are about 90% full. Spoon 1/2 teaspoon of the strawberry mixture onto each cheesecake and swirl around with a the tip on a knife.
Bake in center of oven for 30-35 minutes, until set (center may still jiggle a bit, it will firm up). After about 20-25 minutes insert a toothpick into the center of a cheesecake; if it comes out sticky they are still raw, if it comes out crumby and dry they are done. Remove from oven and allow to cool for at least 30 minutes before attempting to remove the cupcake liners. These cheesecakes taste best after they have been refrigerated.