This research presents a dynamic level control algorithm to meet simultaneously multiple desired tasks based on their allocated priorities for redundant robotic systems. It is shown that this algorithm can be treated as a general framework to achieve control over the whole body of the robot. The control law is an extension of the well-known acceleration based control to redundant robots, and considers also possible interactions with the environment at any point of the robot body. The stability of this algorithm is proven and some of the previously developed methods are formulated using this approach. To control the interaction on the robot body, null space impedance control is developed within the multi-priority framework. Furthermore, the problem of task space control, while guaranteeing a compliant behavior for the redundant degrees of freedom, is considered. This issue may arise in the case where the robot experiences an interaction on its body, especially in the presence of humans. The proposed approach guarantees accurate task execution and compliance of the robot body during intentional or accidental interaction, simultaneously. The asymptotic stability of the task space error is ensured by using suitable observers for estimating and compensating the generalized forces acting on the task variables, without using joint torque measurements. Two different controller-observer algorithms are designed based on the task space error and the generalized momentum of the robot. The performance of the proposed algorithms is evaluated by numerical simulations as well as experiments on a 7R KUKA lightweight robot arm. Keywords: Redundant robots, Multi-priority control, Null space impedance control, Physical human-robot interaction.