If scale invariance exists in nature, the so-called "unparticle physics" may become part of reality. The only way to refute or confirm this idea is through experiments, such as those at the Large Hadron Collider (LHC). One of the peculiar properties of the unparticle stuff is that it gives striking multiphoton signals which have been studied through only the unparticle self-interactions. By considering not only the selfinteractions of unparticles but also all the other possible contributions, which are dominant, a detailed study of the processes, within a scalar unparticle scenario, pp -> 4 gamma, pp -> 2 gamma 2g, pp -> 2 gamma 2l, pp -> 4e, pp -> 4 mu and pp -> 2e2 mu at root s = 14 TeV at the LHC is carried out. We use basic selection cuts and analyze various distributions to discriminate the signals over the Standard Model backgrounds and discuss what seems to be the most likely channel among the above for an indirect manifestation of unparticle effects. We follow a new approach to tackle the issue with the three-point correlation function for the scalar unparticle self-interactions. We also obtain the exclusion region in the unparticle parameter space from the available two-photon data of the LHC and compare it with the existing bounds coming from other sources.