In this work we present some driving strategies for a type of omnidirectional mobile robot, the offset-differential robot. This system presents omnidirectionality while using any type of standard wheels, allowing for applications in all terrain. The work is based on the full kinematic and dynamic analysis of the robot, including the passive elements, to explain some unexpected behaviors that appear during its motion. The stable and unstable behaviors are characterized and some driving strategies are stated in order to achieve the desired performance regarding precise positioning and speed.