Line a baking sheet with parchment paper and set aside.
In a microwave-safe bowl, melt the white chocolate chips in 30-second intervals, stirring after each interval until smooth. If the chocolate is too thick, add vegetable oil to thin it out.
Dip each Oreo cookie into the melted white chocolate, using a fork to fully coat it. Allow excess chocolate to drip off before placing the cookie on the prepared baking sheet.
Repeat the dipping process with all Oreo cookies, then place the baking sheet in the refrigerator for about 15 minutes to set the chocolate.
While the white chocolate is setting, melt the red and blue candy melts in separate microwave-safe bowls, also in 30-second intervals, stirring until smooth.
Once the white chocolate has set, drizzle the melted red and blue candy melts over the cookies using a fork or a piping bag. Immediately sprinkle with red, white, and blue sprinkles.
Return the cookies to the refrigerator for an additional 10 minutes to set the drizzles.