High-quality-factor optical microresonators have emerged as a verstatile tool in studying light-matter interactions and their technological applications. They have proven to be particularly efficient sensors by transducing weak interactions, such as a minuscule change in effective refractive index, into a large optical output signal, when interrogated near their resonance frequencies. Their large quality factors and small sizes also lead to a build-up of large optical forces within the devices. These forces are a driver of high-quality mechanical oscillations of the optical resonator. The resolution of accelerometers is limited by fundamental thermomechanical noise and by extra noise added by the readout mechanism. We present a platform based on SiN optical microresonators with a high quality factor (Q), which can be used as highly sensitive displacement sensors to minimise readout noise in accelerometers. In addition, we demonstrate integration of SiN micromechanical resonators, which also potentially demonstrate very high quality factors, with a large micromachined mass, which can be used to lower thermomechanical noise in accelerometers. The SiN ring resonator with the SiN micromechanical resonators together can potentially measure acceleration with nano-g resolution over a broad bandwidth. Frequency-locking between mechanical oscillators is of scientific and technological importance. However, existing schemes to observe such behaviour are not scalable over distance. We demonstrate a scheme to couple two independent mechanical oscillators, separated in frequency by 80 kHz and situated far from each other (3.2 km), via their optomechanical interactions. Using light as the coupling medium enables this scheme to have low loss and be extended over long distances. Delay-coupled oscillators exhibit unique phenomena that are not present in systems without delayed coupling. We experimentally demonstrate mutual synchronisation of two free-running micromechanical oscillators, coupled via light with a total delay 139 ns (approximately four and a half times the mechanical oscillation time period). This coupling delay induces multiple stable states of synchronised oscillations, each with a different oscillation frequency. These states can be accessed by varying the coupling strengths. This result could enable applications in reconfigurable radio-frequency networks, and novel computing concepts.