Integrated sensing, communications and computing (ISCC) system has been emerged as a crucial paradigm for addressing the growing demand of emerging wireless applications that require both ultra-reliable low-latency computing and high-precision sensing. In this paper, we investigate a non-orthogonal multiple access (NOMA)-assisted integrated sensing and two-tier task offloading (ISTTO) system in which the multi-functional access point (AP) provides task offloading services for a group of edge computing users via NOMA while performing sensing towards a target. To balance the utilization of the computing resources across different tiers, the AP can further offload part of the received workloads to a group of cloudlet servers. To investigate this problem, we formulate a joint optimization of the AP's transmit beamforming, the two-tier dedicated sensing signals, the two-tier computation offloading strategies and the associated allocations of the communication and computing resources, with the objective of minimizing the total energy consumption, while guaranteeing the required sensing performance over the total duration. Although the formulated joint optimization problem is strictly non-convex, we identify the features of its solutions and exploit a decomposition-based framework for solving it. Numerical results validate the accuracy and effectiveness of our proposed algorithm and show the performance advantages of our NOMA-assisted ISTTO scheme. Compared with several benchmark schemes, our NOMA-assisted ISTTO scheme achieves better performances in both sensing and task offloading, while suppressing the interference from undesired directions.