To meet the surging demands on network throughput and spectrum resources arising with billions of Internet-of-Things mobile devices (IMDs), ultradense networks are envisioned to be a promising technology, which gives rise to the so-called ultradense Internet-of-Things (IoT) networks. Meanwhile, with the constant emergence of new IoT applications, the conflict between computing-intensive applications and resource-constrained IMDs is increasingly prominent. By offloading computing-intensive tasks to the edge servers in close proximity, mobile-edge computing is expected as an effective solution to address this issue. However, computation offloading research in ultradense IoT networks is still scarce until now. Toward this end, we provide this paper to study the energy-aware task offloading problem with multiple edge servers in ultradense IoT networks, where diverse kinds of computation tasks are randomly requested by the IMDs and the computing resources at the edge servers change dynamically. An iterative searching-based task offloading scheme is proposed as our solution, which jointly optimizes task offloading, computational frequency scaling, and transmit power allocation. Extensive numerical results demonstrate the superior performance of conducting task offloading among multiple edge servers, and corroborate the advantages of our scheme over existing works which either fixed computational frequency and transmit power, or neglected the impact of the IMDs' residual battery.