We report a comprehensive investigation of the effects of quantum turbulence and quantized vorticity in superfluid $^4$He on the motion of a micro-electromechanical systems (MEMS) resonator. We find that the MEMS is uniquely sensitive to quantum turbulence present in the fluid. To generate turbulence in the fluid, a quartz tuning fork (TF) is placed in proximity to the MEMS and driven at large amplitude. We observe that at low velocity, the MEMS is damped by the turbulence, and that above a critical velocity, $v_c simeq 5,$mm,s$^{-1}$, the turbulent damping is greatly reduced. We find that above $v_c$, the damping of the MEMS is reduced further for increasing velocity, indicating a velocity dependent coupling between the surface of the MEMS and the quantized vortices constituting the turbulence. We propose a model of the interaction between vortices in the fluid and the surface of the MEMS. The sensitivity of these devices to a small number of vortices and the almost unlimited customization of MEMS open the door to a more complete understanding of the interaction between quantized vortices and oscillating structures, which in turn provides a new route for the investigation of the dynamics of single vortices.