Dissipative Kerr soliton microcombs have inspired various intriguing applications such as spectroscopy, ranging, telecommunication, and high purity microwave generation. Mechanically actuated soliton microcombs provide enhanced controllability and flexibility for Kerr solitons, thus enabling technological progress to be made on such practical applications. Here, we present architectures for coherent dual-comb techniques and ultralow-noise microwave generation by exploiting the mechanical actuation of ultrahigh-Q crystalline microresonators. By unifying a pump laser, we demonstrate highly coherent dual-soliton combs using distinct resonators with slightly different repetition rates. We also report significant phase-noise reduction achieved by directly generating Kerr solitons from a sub-Hz linewidth ultrastable laser. This study paves the way for further advancements in a wide variety of applications based on Kerr soliton microcombs.