Stencil computation is an extensively-utilized class of scientific-computing applications that can be efficiently accelerated by graphics processing units (GPUs). Out-of-core approaches enable a GPU to handle large stencil codes whose data size is beyond the memory capacity of the GPU. However, current research on out-of-core stencil computation primarily focus on minimizing the amount of data transferred between the CPU and GPU. Few studies consider simultaneously optimizing data transfer and kernel execution. To fill the research gap, this work presents a synergy between on-and off-chip data reuse for out-of-core stencil codes, termed SO2DR. First, overlapping regions between data chunks are shared in the off-chip memory to eliminate redundant CPU-GPU data transfer. Secondly, redundant computation at the off-chip memory level is intentionally introduced to decouple kernel execution from region sharing, hence enabling data reuse in the onchip memory. Experimental results demonstrate that SO2DR significantly enhances the kernel-execution performance while reducing the CPU-GPU data-transfer time. Specifically, SO2DR achieves average speedups of 2.78× and 1.14× for five stencil benchmarks, compared to an out-of-core stencil code which is free of redundant transfer and computation, and an in-core stencil code which is free of data transfer, respectively.