This paper focuses on the development of a dynamic model-free whole-body controller for a humanoid robot with high kinematic redundancy. The proposed controller is based on force-level operational-space control framework, which computes joint torques for the required forces of prioritized multiple tasks. While typical approaches based on this framework require to obtain an accurate robot dynamics model, which has been generally recognized as a major hurdle to overcome for implementation in real humanoid robots, the proposed controller incorporates adaptive sliding-mode and online dynamics estimation schemes; thus, it can be easily realized on a humanoid without identifying complex robot dynamic parameters. As a result, the gains of the proposed controller are adaptively adjusted to assure the control accuracy, when the humanoid robot changes its posture and undergoes uncertain disturbances. Experiments with a 23-DoFs humanoid under uncertain disturbances verify that the proposed controller can robustly perform multiple tasks with high accuracy.