Preheat the oven to 350 degrees F. Grease a 9x13-inch cake pan.
In a medium bowl, make the cake mix according to package directions. Pour it into the prepared pan and bake according to the directions on the box. Cool completely.
In a medium bowl, whisk together the pudding mix and milk until thick. Stir in the Cool Whip.
Cut one-third of the cake into 1-inch cubes and place them into the bottom of a large trifle bowl. Spoon one third of the pudding mixture on top, spreading to the edges.
Pulse one third of the Oreos in a food processor until they are in fine crumbs. Spread the Oreos over the pudding.
Repeat the layers two more times, ending with the Oreo crumbs.
Refrigerate until ready to serve.
For serving, press wooden skewers into the bottom of the Peeps Bunnies so that they will stand up straight. Press them into the top of the Dirt Cake. Add Easter candy or sprinkles for decoration.