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We propose energy-efficient voltage-induced strain control of a domain wall (DW) in a perpendicularly magnetized nanoscale racetrack on a piezoelectric substrate that can implement a multistate synapse to be utilized in neuromorphic computing platforms. Here, strain generated in the piezoelectric is mechanically transferred to the racetrack and modulates the perpendicular magnetic anisotropy (PMA) in a system that has significant interfacial Dzyaloshinskii-Moriya interaction (DMI). When different voltages are applied (i.e., different strains are generated) in conjunction with spin-orbit torque (SOT) due to a fixed current flowing in the heavy metal layer for a fixed time, DWs are translated to different distances and implement different synaptic weights. We have shown using micromagnetic simulations that five-state and three-state synapses can be implemented in a racetrack that is modeled with the inclusion of natural edge roughness and room temperature thermal noise. These simulations show interesting dynamics of DWs due to interaction with roughness-induced pinning sites. Thus, notches need not be fabricated to implement multistate nonvolatile synapses. Such a strain-controlled synapse has an energy consumption of ~1 fJ and could thus be very attractive to implement energy-efficient quantized neural networks, which has been shown recently to achieve near equivalent classification accuracy to the full-precision neural networks.