This paper proposes a novel Hierarchical Quadratic Programming (HQP)-based framework that enables multi-tasking control under multiple Human-Robot Interaction (HRI) scenarios. The objective is to create a unique framework for various types of HRI control modalities, avoiding the necessity of switching between different controllers that are usually tailored to a specific task. To achieve this, we firstly propose a HQP-based hybrid Cartesian/joint space impedance control formulation. This is based on the system's dynamics and provides an adaptive compliance behaviour during HRI, while performing hierarchical motion control. This is validated through a series of experiments that show the accuracy of trajectory tracking and the variable compliance behaviour. We then consider the case in which the human needs to move the robot by acting directly onto it, by proposing a hybrid admittance/impedance hierarchical control, which is then validated through several experiments in which the human moves the robot in the workspace. Next, we formulate a HQP-based force controller for HRI applications in which a specific interaction force must be maintained and lastly, we extend this to simultaneous force and trajectory tracking for applications that need higher position accuracy. Further experiments are conducted, to validate the proposed framework, using a redundant mobile manipulator. Overall, we obtain a single multi-purpose HQP-based control framework, that can switch continuously between interaction modes, enclosing multiple behaviours adjusted online based on the type of interaction.