Due to the swift advancement of edge computing and mobile crowdsensing (MCS), edge-assisted MCS (EAMCS) has emerged as a promising paradigm, leveraging sensor-embedded mobile devices for the collection and sharing of environmental data. As the sensing scale increases in the modern urban, the application scenario becomes more and more complex, and the budget of users and platform is limited. Therefore, it is indispensable to study the effective task allocation mechanism with considering the multiple budget constraints in the EAMCS system. However, a majority of the existing studies unilaterally focus on either the users’ time budget or the platform’s budget, disregarding the crucial aspect of the users’ energy budget. In this article, we design a joint user movement, sensing, offloading, and computation framework adopting the computation offloading strategy called binary processing strategy. In addition, the multitask data collection with a limited budget (MDCB) problem considering time, energy, and platform budget in EAMCS is formulated, which is proved to be nondeterministic polynomial-hard. In order to maximize the amount of data collected by the users in the MDCB problem, we first verify the submodularity of the objective function, then propose the global maximum data first search algorithm and task sequence-based genetic algorithm to solve the problem. The extensive experiments are conducted on both synthetic and real-world data sets to demonstrate the effectiveness of our proposed schemes.