Surface acoustic wave (SAW) devices are generally fabricated on rigid substrates that support the propagation of waves efficiently. Although very challenging, the realisation of SAW devices on bendable and flexible substrates can lead to new generation SAW devices for wearable technologies. In this paper, we report flexible acoustic wave devices based on ZnO thin films coated on various substrates consisting of thin layers of metal (e.g., Ni/Cu/Ni) and/or polymer (e.g., polyethylene terephthalate, PET). We comparatively characterise the fabricated SAW devices and demonstrate their sensing applications for temperature and ultraviolet (UV) light. We also investigate their acoustofluidic capabilities on different substrates. Our results show that the SAW devices fabricated on a polymer layer (e.g. ZnO/PET, ZnO/Ni/Cu/Ni/PET) show enhanced temperature responsivity, and the devices with larger wavelengths are more sensitive to UV exposure. For actuation purposes, the devices fabricated on ZnO/Ni/Cu/Ni layer have the best performance for acoustofluidics, whereas insignificant acoustofluidic effects are observed with the devices fabricated on ZnO/PET layers. We propose that the addition of a metallic layer of Ni/Cu/Ni between ZnO and polymer layers facilitates the actuation capability for the acoustofluidic applications while keeping temperature and UV sensing capabilities, thus enhancing the integration of sensing and acoustofluidic functions.