This paper proposes to integrate our prioritized impedance controller (PIC) into four kinds of improved hierarchical operational-space torque-control frameworks: one pseudo-inverse-based dynamics method and three optimization-based techniques, including one null-space-based weighted optimization solver, one hierarchical optimization solver, and one hybrid hierarchical-weighted solver. The integrated PIC enables various impedance control forces to be consistent and compatible with multi-task hierarchies. The concept PIC can handle more general impedance controllers, including those built directly on specifically designed tasks and those indirectly acting on the whole-body behaviors. In the pseudo-inverse-based dynamics method and the null-space-based weighted scheme, each task acceleration with the prioritized impedance controller is extracted using one proposed modified dynamics model embodying PIC, which especially enables the integration of this new prioritized weighted scheme in the strict hierarchical control framework. For the hierarchical optimization solver, another modified dynamics model is proposed to integrate PIC and embody the multi-level control hierarchy. The second modified dynamics model makes it possible to achieve a more general and complete hierarchical optimization solver for both the task acceleration extraction and the same number of constraints for each hierarchy, expressed depending on the actuated torque. Then we use our second modified model for a more complex scenario, combining the hierarchical and the null-space-based weighted frameworks together. The two dynamics models are only developed for the derivation of the relative torque controllers, and the detailed algorithm is developed which is more general and compact for the three optimization solvers. Any of the approaches can be selected depending on the actual user-defined applications. Our methods are tested and compared in several simulation scenarios using a virtual quadruped-on-wheel robot, TowrISIR with a manipulator on its floating base.