The multi-access edge computing (MEC) and ultra-dense network (UDN) are regarded as essential and complementary technologies in the age of Internet of Things (IoT). Deploying MEC servers at the macro-cell and small-cell stations can significantly improve user experience as well as increase network capacity. Nevertheless, there still remain many obstacles in practical MEC-enabled UDNs. Among them, a unique challenge is how to coordinate computing and networking to fit the diverse offloading demands of IoT applications in dynamic network environments. To this end, this paper first investigates a distributed delay-constrained computation offloading methodology based on computing and networking coordination in the UDN. An extended game-theoretic approach based on the Lyapunov optimization theory is designed to achieve adaptive task offloading and computing power management in time-varying environments. Furthermore, considering the uncertainty in users’ mobility and limited edge resources, distributed two-stage and multi-stage stochastic programming algorithms under various uncertainties are proposed. The proposed algorithms take posterior recourse actions to compensate for inaccurate predicted network information. Extensive simulations validate the effectiveness and rationality of the proposed algorithms and their superior performance over several benchmark schemes.