Mobile edge computing (MEC) can dramatically promote the computation capability and prolong the lifetime of mobile users (MUs) by offloading computation-intensive tasks to edge cloud. In this paper, a spatial-random two-tier heterogeneous network (HetNet) is modelled to feature random node distribution, where the small-cell base stations (SBSs) and the macro base stations (MBSs) are cascaded with servers with different levels of computing and storage capacity. Only a certain type of application services and finite number of offloaded tasks can be cached and processed in the resource-limited edge server. For that setup, we investigate the performance of two offloading strategies corresponding to integrated access and backhaul (IAB)-enabled MEC networks and traditional cellular MEC networks. Using tools from stochastic geometry and queuing theory, we derive the average delay for the two different strategies, in order to better understand the influence of IAB on MEC networks. Simulations results are provided to verify the derived expressions and to reveal various system-level insights.