This paper proposes a security-aware computation offloading framework tailored for mobile edge computing (MEC)enabled Internet of Things (IoT) networks operating in environments with aerial eavesdroppers (AEs) and ground eavesdroppers (GEs). It is envisaged that multiple ground nodes (GNs) should perform computation tasks partly locally and partly remotely by offloading a portion of these tasks to MEC servers. To facilitate this paradigm, an unmanned aerial vehicle (UAV) is deployed, serving as both an aerial MEC server and a relay for forwarding part of the tasks to a ground access point (AP) for computing. The computation offloading is further reinforced by incorporating a reconfigurable intelligent surface (RIS) unit in close proximity to the AP. Within this context, this paper provides an analysis of the secrecy outage probability (SOP) and formulates an optimization problem aimed at maximizing the minimum secure computation efficiency (SCE) by jointly optimizing transmit power allocation, time slot scheduling, task allocation, and RIS's phase shifts. Given the non-convex nature of the problem, an iterative algorithm is introduced to address the fractional objective function and coupled optimization variables by employing Dinkelbach-and block coordinate descent (BCD)-based methods, respectively. The obtained results confirm the efficacy of the optimized scheme.