Preheat oven to 300º F. Place a pan of hot water on the bottom rack of your oven.
Mix cracker crumbs, sugar, and butter. Pat into bottom and up sides of 2 (4-inch) cheesecake springform pans. Set aside.
Mix cream cheese, condensed milk, sugar, and cornstarch until well blended. Add eggs, one at a time, and beat well. Add lemon juice, and vanilla until well blended. Add sour cream and beat for 1 1/2 minutes.
Pour half of mixture into prepared crusts. Place 2 Oreos over mixture. Pour remaining half of mixture over Oreos. Place in oven and bake for 45 minutes. Turn off oven, open oven door, and let cakes remain in open oven for 1 hour. Remove from oven. Once cakes are cool, refrigerate for 4 hours or overnight.
Remove from refrigerator and remove from springform pans.