Intelligent reconfigurable surface (IRS) is an emerging technology for the enhancement of spectrum and energy efficiency. We propose a novel IRS-and-unmanned aerial vehicle (UAV)-Assisted mobile edge computing (MEC) framework, where a MEC server installing on an UAV to facilitate task calculations by mobile users (MUs), and an IRS modulates channels between MUs and the UAV. Non-orthogonal multiple access (NOMA) is employed for further improving system-wide spectral efficiency. There are needs for joint optimization of multiple parameters, e.g., the task partition parameters and the transmit power of all MUs, the reflection coefficient matrix of the IRS and the movement trajectory of the UAV, and such needs raises the challenge of minimizing the long-term total energy consumption of all MUs while satisfying required transmission rate and task completion delay. We divide optimization tasks into two sub-problems and propose specific solutions respectively, i.e., relevant decisions about the UAV and MUs to be solved by deep reinforcement learning (DRL); and the reflection coefficient matrix of the IRS to be solved by block coordinate descent (BCD). A series of experiments have verified the effectiveness of the proposed communication techniques and optimization algorithms. Simulation results demonstrate that (1) NOMA-IRS technique achieves better energy efficacy compared to the cases where random IRS or no IRS is deployed and the conventional orthogonal multiple access (OMA) technique with IRS. (2) our proposed deep deterministic policy gradient (DDPG)-BCD algorithm outperforms other four benchmark algorithms in solving the complex and dynamic optimization problem.