This paper presents a novel modular robot system that can self-reconfigure to achieve omnidirectional movements for collaborative object transportation. Each robotic module is equipped with a steerable omni-wheel for navigation and is shaped as a regular icositetragon with a permanent magnet installed on each corner for stable docking. After aggregating multiple modules and forming a structure that can cage a target object, we have developed an optimization-based method to compute the distribution of all wheels’ heading directions, which enables efficient omnidirectional movements of the structure. By implementing a hierarchical controller on our prototyped system in both simulation and experiment, we validated the trajectory tracking performance of an individual module and a team of six modules in multiple navigation and collaborative object transportation settings. The results demonstrate that the proposed system can maintain a stable caging formation and achieve smooth transportation, indicating the effectiveness of our hardware and locomotion designs.