Line a large sheet pan with parchment paper and set aside.
Place whole Oreo cookies (don't separate cookie from creme) in a blender or food processor. Pulse until they have been crushed into fine crumbs. Ensure there are no large pieces and transfer all but 2 tablespoons (set aside for later) to a large bowl or stand mixer.
Add the softened cream cheese (important it isn't too cold or melty) to the remaining Oreo crumbs. Using a hand mixer or the whisk attachment on a stand mixer, beat until ingredients are well combined and smooth. (If you don't have a mixer, knead with your hands until smooth and combined.)
Scoop Oreo "dough" by tablespoonsful (I like smaller balls so the ratio of Oreo to chocolate is bigger, but feel free to make them larger) and knead the balls until you can roll into a smooth and even ball. Repeat with all the dough until it is all rolled in balls.
Place in fridge or freezer and chill for 15 to 20 minutes.
Place dark, milk, or semi-sweet chocolate in microwave-safe bowls. Melt the chocolate in bursts of 15 seconds, stirring in between each burst for 15 seconds until chocolate is completely smooth. Be careful to not burn/scorch the chocolate-- a lot of melting happens out of the microwave. Add some oil if needed to thin. (I usually add about 1/4 to 1/2 teaspoon per cup of chocolate.) Stir until smooth.
Remove Oreo Balls from the fridge/freezer and dip them in chocolate. Place one chilled ball on a large fork and spoon melted chocolate right over the ball. Tap that fork against the bowl a few times to help the chocolate smooth out and then slide the fork against the edge of the bowl to remove excess. Use a table knife to gently slide the ball off the fork and onto the prepared parchment paper-lined tray. Repeat until all the truffles are dipped in chocolate. If the melted chocolate is getting too hard to dip, put in the microwave for another 15 seconds and remix. Sprinkle reserved 2 tablespoons of Oreo crumbs over half of the truffles.
For the remaining truffles, add a white chocolate drizzle (optional): add the white chocolate (and 1/4 to 1/2 teaspoon oil if desired, to make it easier to work with) to a microwave-safe bowl and microwave in bursts of 15 seconds, stirring in between each burst for 15 seconds until smooth. Transfer the melted white chocolate into a plastic bag and seal it. Cut off the very tip with scissors and pipe through the bag in stripes across the Oreo balls.
Allow chocolate to harden before serving. Keep any leftover Oreo Balls stored in an airtight container in the fridge.