The structural reorganization of the actin cytoskeleton is facilitated through the action of motor proteins that crosslink the actin filaments and transport them relative to each other. Here, we present a combined experimental-computational study that probes the dynamic evolution of mixtures of actin filaments and clusters of myosin motors. While on small spatial and temporal scales the system behaves in a very noisy manner, on larger scales it evolves into several well distinct patterns such as bundles, asters and networks. These patterns are characterized by junctions with high connectivity, whose formation is possible due to the organization of the motors in 'oligoclusters' (intermediate-size aggregates). The simulations reveal that the self-organization process proceeds through a series of hierarchical steps, starting from local microscopic moves and ranging up to the macroscopic large scales where the steady-state structures are formed. Our results shed light on the mechanisms involved in processes such as cytokinesis and cellular contractility, where myosin motors organized in clusters operate cooperatively to induce the structural organization of cytoskeletal networks.