Quantum devices for sensing and computing applications require coherent quantum systems which can be manipulated in a fast and robust way. Such quantum control is typically achieved using external electric or magnetic fields which drive the system's orbital or spin degrees of freedom. However, most of these approaches require complex and unwieldy antenna or gate structures, and with few exceptions are limited to the regime of weak driving. Here, we present a novel approach to strongly and coherently drive a single electron spin in the solid state using internal strain fields in an integrated quantum device. Specifically, we study individual Nitrogen-Vacancy (NV) spins embedded in diamond mechanical oscillators and exploit the intrinsic strain coupling between spin and oscillator to strongly drive the spins. As hallmarks of the strong driving regime, we directly observe the energy spectrum of the emerging phonon-dressed states and employ our strong, continuous driving for enhancement of the NV spin coherence time. Our results constitute a first step towards strain-driven, integrated quantum devices and open new perspectives to investigate unexplored regimes of strongly driven multi-level systems and to study exotic spin dynamics in hybrid spin-oscillator devices.