In this paper, we study caching, transmission, and phase-shift techniques applied to unmanned aerial vehicles (UAV) mounted intelligent reflecting surfaces (IRS) system for video multicasting in edge content delivery networks (eCDN). To assist the eCDN, the UAV caches a proper set of videos, and then flies to serve the end users (EU) in different clusters. Besides being served by direct transmission mode from the UAV with cached videos, the EUs can receive the requested videos from macro base station via the UAV-mounted IRS by reflecting transmission mode. In this scenario, we formulate a joint caching, transmission mode selection, and phase-shift (CMP) optimization problem. The CMP optimization problem is solved to maximize the sum rate by finding the optimal results of which videos to cache, what transmission modes to select, and how to adjust the phase-shift values for multicasting. Simulation results are shown to demonstrate the advantages of the proposed CMP method compared to other conventional benchmarks with detailed discussions and analyses.