The phenomenon of ferromagnetic resonance (FMR) provides fundamental information on the physics of magnetic materials and lies at the heart of a variety of signal processing microwave devices. Here we demonstrate theoretically that substrate-induced lattice strains may change the FMR frequency of an epitaxial ferromagnetic film dramatically, leading to ultralow and ultrahigh resonance frequencies at room temperature. Remarkably, the FMR frequency varies with the epitaxial strain nonmonotonically, reaching minimum at a critical strain corresponding to the strain-induced spin reorientation transition. Furthermore, by coupling the ferromagnetic film to a ferroelectric substrate, it becomes possible to achieve an efficient voltage control of FMR parameters. In contrast to previous studies, we found that the tunability of FMR frequency varies with the applied electric field and strongly increases at critical field intensity. The revealed features open up wide opportunities for the development of advanced tunable magnetoelectric devices based on strained nanomagnets.