This paper presents a multi-functional system, consisting of a magnetorheological (MR) damper and an electromagnetic induction (EMI) device, and its applications in stay cables. The proposed system is capable of offering multiple functions: (I) mitigating excessive vibrations of cables, (2) estimating cable tension, and (3) harvesting energy for wireless sensors used health monitoring of cable-stayed bridges. In the proposed system, the EMI device, consisting of permanent magnets and a solenoid coil, can converts vibration energy into electrical energy (i.e., induced emf); hence, it acts as an energy harvesting system. Moreover, the cable tension can be estimated by using the emf signals obtained from the EMI device. In addition, the MR damper, whose damping property is controlled by the harvested energy from the EMI device, can effectively reduce excessive cable vibrations. In this study, the multi-functionality of the proposed system is experimentally evaluated by conducting a shaking table test as well as a full-scale stay cable in a laboratory setting. In the shaking table experiment, the energy harvesting capability of the EMI device for wireless sensor nodes is investigated. The performance on the cable tension estimation and the vibration mitigation are evaluated using the full-scale cable test setup. The test results show that the proposed system can sufficiently generate and store the electricity for operating a wireless sensor node twice per day, significantly alleviate vibration of a stay cable (by providing about 20% larger damping compared to the passive optimal case), and estimate the cable tension accurately within a 2.5% error.