In a large microwave-safe bowl, combine glutinous rice flour, sugar, cornstarch, milk, and red food coloring. Mix until smooth. Cover with plastic wrap and microwave for 2 minutes. Stir and microwave again for 2 minutes, repeating until glossy and sticky, about 4 to 6 minutes total.

Allow the mochi dough to cool slightly before adding vegetable oil. Knead until smooth and elastic, about 2 minutes. Divide into 14 equal pieces, shaping each into a disk dusted with cornstarch.

In a mixing bowl, beat Philadelphia cream cheese and lemon juice until creamy. Gradually add sugar and vanilla extract, mixing until fully incorporated. Whip heavy cream until stiff peaks form; gently fold into cream cheese mixture.

Take one disk of mochi, add cheesecake filling and strawberries to the center. Fold the edges over the filling, sealing tightly. Repeat with remaining disks.

Chill the assembled mochis in the refrigerator for 3 to 4 hours until the filling is set and the exterior is firm.