Electromagnetic damper (EMD), which has shown good vibration isolation and energy harvesting potential, has received much attention in recent years. In addition, the harvested energy of EMD systems can be used to further suppress severe vibration. When the harvested energy of the suspension system is more than the consumed energy, the suspension system can realize self-powered functions. However, the integration of the above three functions is a challenge for the design of EMD systems. In this paper, a novel multi-function electromagnetic damper (MFEMD) system, which integrates the semi-active vibration control mode, energy-harvesting mode, and self-powered mode, is introduced first. The MFEIS system applies an H-bridge circuit to control the multi-directional flow of circuit energy flow, and the supercapacitor is used as the energy storage device because of its high-power density and rapid response speed. Since vehicles are driving in complex road conditions in the real world, road information needs to be considered to control the MFEMD system. Additionally, the energy recovery efficiency and vibration suppression performance of the MFEMD system also need to be balanced. A switchable control strategy based on road classification is proposed to switch the state of the MFEMD system. According to the real driving conditions, roads are classified into three categories, namely high-speed smooth roads, medium-speed good roads, and low-speed bad roads. The state of the MFEMD system is switched based on the road information to balance the ride comfort and energy recovery efficiency. A complex road, which contains different levels of random roads, is adopted to verify the effectiveness of the proposed control strategy. Simulation results verified the effectiveness of the proposed switchable control strategy compared with a well-tuned passive suspension and a semi-active suspension.