Beat the cream cheese. In a large bowl, beat the cream cheese with an electric mixer until light and fluffy, about 30 seconds to 1 minute.
Add the pudding mix and milk. Add the dry pudding mix and about ¼ cup of the milk. Mix until well combined. The mixture will be very thick at first, which is fine. Gradually add the remaining milk, mixing constantly, until smooth (a few small lumps are okay).
Swirl in the jam. Dollop the jam over the filling by the tablespoonful. Use a knife to gently swirl it into the pudding mixture. Streaks of jam are good, it doesn't need to be fully combined.
Fold in the Cool Whip. Gently fold in half of the Cool Whip, being careful not to deflate it.
Prep the strawberries. Pat the sliced strawberries dry with a paper towel to keep them from bleeding into the filling.
Start the layers. Spread about ¼ cup of the pudding mixture in a thin layer in the bottom of a deep 8-inch or 9-inch square dish. Add a layer of graham crackers, breaking them as needed to fit.
Build up the cake. Spread ⅓ of the remaining pudding mixture over the graham crackers, then top with ⅓ of the strawberries. Repeat the layers twice more to use up the graham crackers, pudding, and strawberries.
Top with Cool Whip and chill. Spread the remaining half of the Cool Whip on top. Cover and refrigerate for at least 4 hours, or overnight. Garnish with additional sliced strawberries just before serving.