Skyrmions, as nonlinear topological solitons, have garnered significant attention due to their unique physical properties and promising potential for applications. However, achieving controlled manipulation of skyrmion arrays remains a formidable challenge. Here, we introduce a SAW-mediated strategy to engineer well-ordered skyrmion configurations within ferromagnetic [Co/Pd]n multilayer nano-islands. We exploit radially propagating SAWs generated by fan-shaped interdigital transducers to achieve controlled spatial ordering of skyrmions. The ordering arises from SAW-induced anisotropic strain gradients, which create periodically modulated potential landscapes. Quasi-static analysis reveals the critical role of magnetoelastic coupling, enabling strain-amplitude-dependent lattice transitions and wavelength-selective ordering. Furthermore, pulsed SAWs implement a neuromorphic synapse-inspired design emulating long-term potentiation, achieving 94.6% accuracy on CIFAR-10. This work not only provides an effective strategy for controlling skyrmion arrangement in confined nano-islands but also offers valuable insights for the device integration of skyrmions.