This manuscript presents an overview of my research activities in the study ofthe multimode coupling in microwave optomechanical circuits and phononcavitynanomechanics, and the topics that will be pursued based on currentadvances. The studies start with the experimental realisation of a microwaveoptomechanical platform to investigate on-chip phonon thermometryin a single-tone pumping scheme and optomechanically induced transparency/amplifications in a double-tone driving scheme. The same physicsand experimental techniques are then transferred in investigations of mechanicalphonon-phonon interactions in phonon-cavity nanomechanics, consistingof two distinct and capacitively coupled membrane resonators, analogous tooptomechanics. To understand how energy is coherently transferred in coupledmultimodes, semi-classical and classical models of microwave optomechanicalcircuits and phonon-cavity systems have been developed according todifferent drive configurations. In addition, by integrating microwave interferometrywith a scanning tip, I have experimentally extended the applicationsof scanning microwave microscopy to image mechanical vibration modes of amembrane. Using these mode coupling techniques, the energy, in the form ofphonons, can be coherently transferred between the scanning tip and its coupledmembrane resonators. These experimental results are based not only onour efforts in theoretical analysis, but also on advanced microwave setups andnovel silicon nitride membrane nanoelectromechanical systems developed byusing advanced nanofabrication techniques. These achievements and accumulatedtechniques allow ongoing research activities to focus on the explorationof computational functions and quantum sensing in coupled mechanical resonatorsand microwave optomechanical systems.