A new model of physics, with a hidden conformal sector which manifests itself as an unparticle coupling to standard model particles effectively through higher dimensional operators, predicts strong collider signals due to unparticle self-interactions. We perform a complete analysis of the most spectacular of these signals at the hadron collider, pp(p)->gamma gamma gamma gamma and gamma gamma gg. These processes can go through the three-point unparticle self-interactions as well as through some s and t channel diagrams with one and/or two unparticle exchanges. We study the contributions of individual diagrams classified with respect to the number of unparticle exchanges and discuss their effect on the cross sections at the Tevatron and the LHC. We also restrict the Tevatron bound on the unknown coefficient of the three-point unparticle correlator. With the availability of data from the Tevatron, and the advent of the data emerging from the LHC, these interactions can provide a clear and strong indication of unparticle physics and distinguish this model from other beyond the standard model scenarios.