Various musculoskeletal humanoids have been developed so far. While these humanoids have the advantage of their flexible and redundant bodies that mimic the human body, they are still far from being applied to real-world tasks. One of the reasons for this is the difficulty of bipedal walking in a flexible body. Thus, we developed a musculoskeletal wheeled robot, Musashi-W, by combining a wheeled base and musculoskeletal upper limbs for real-world applications. Also, we constructed its software system by combining static and dynamic body schema learning, reflex control, and visual recognition. We show that the hardware and software of Musashi-W can make the most of the advantages of the musculoskeletal upper limbs, through several tasks of cleaning by human teaching, carrying a heavy object considering muscle addition, and setting a table through dynamic cloth manipulation with variable stiffness.