This article deals with the task assignment problem for multiple autonomous underwater vehicles to efficiently collect underwater data from sensors. We formulate a unified framework to consistently address the heterogeneous task assignment problem (nonemergency and emergency cases) without strictly distinguishing the mixed cases. First, a unified problem, which bridges the gap between different constraints and optimization objectives of different cases, is constructed. Then, the proposed reinforced self-organizing mapping algorithm is reinforced in three aspects: the regional learning rate, the self-configuring neuron (SCN) strategy, and the workload balance mechanism. Specifically, the proposed regional learning rate comprehensively considers the individual worth of tasks and the topology to generate the regional learning rate of dynamic task regions, which consists of dynamic remaining tasks and the reconstructed topology. Based on this idea, the constructed unified problem can be solved consistently. Furthermore, the proposed SCN strategy optimizes the neuron population both in quality and quantity, and guides the update of neurons with enriched historical information to improve the mapping ability. This strategy greatly improves learning efficiency and applicability in a wide range of scenarios. Meanwhile, the proposed workload balance mechanism takes into consideration of both the work capability and consumed energy to extend the continuous working capability. The numerical results validate the effectiveness and adaptability of the proposed unified task assignment framework.