Wirelessly actuated miniature soft robots actuated by magnetic fields that can overcome gravity by climbing soft and wet tissues are promising for accessing challenging enclosed and confined spaces with minimal invasion for targeted medical operation. However, existing designs lack the directional steerability to traverse complex terrains and perform agile medical operations. Here we propose a rod-shaped millimeter-size climbing robot that can be omnidirectionally steered with a steering angle up to 360 degrees during climbing beyond existing soft miniature robots. The design innovation includes the rod-shaped robot body, its special magnetization profile, and the spherical robot footpads, allowing directional bending of the body under external magnetic fields and out-of-plane motion of the body for delivery of medical patches. With further integrated bio-adhesives and microstructures on the footpads, we experimentally demonstrated inverted climbing of the robot on porcine gastrointestinal (GI) tract tissues and deployment of a medical patch for targeted drug delivery.