Due to the massive computing demands of the Internet of Things, mobile edge computing (MEC) has been extensively investigated as a means of providing computation-intensive and latency-sensitive services at the network edge. With increasing density of base stations (BSs), users are simultaneously served by multiple BSs, leading to the multicell MEC environment. Intelligent reflecting surface (IRS) provides a promising solution for constructing the virtual Line-of-Sight (LoS) links between cell-edge users (CEUs) and BSs. In this article, we investigate the joint channel estimation and resource allocation in the IRS-aided multicell MEC system. Instead of assuming the perfect channel state information (CSI), we propose a three-phase channel estimation method to obtain the CSI. Our purpose is to minimize the total joint energy and latency cost (JELC) in terms of both task-execution latency and energy consumption in the IRS-aided multicell MEC problem by jointly optimizing the task offloading volume, precoding matrix, and IRS phase shifts. We propose a quadratically constrained program (QCP)-assisted proximal policy optimization (PPO) reinforcement learning algorithm with two modules (i.e., QCP optimizer and PPO agent) execute iteratively. The QCP optimizer is utilized to compute the offloading decision variables, and the PPO agent is adapted to determine the optimal channel precoding matrix and the phase shifts of IRS. Numerical results validate that our QCP-assisted PPO algorithm executes more rapidly than benchmarks. Moreover, the proposed QCP-assisted PPO algorithm delivers the best performance compared to benchmarks. Furthermore, the multicell IRS-aided MEC framework yields additional performance gains compared to those without IRS.