Recently, there are increasing efforts on advancing optical neural networks (ONNs), which bring significant advantages for machine learning (ML) in terms of power efficiency, parallelism, and computational speed. With the considerable benefits in computation speed and energy efficiency, there are significant interests in leveraging ONNs into medical sensing, security screening, drug detection, and autonomous driving. However, due to the challenge of implementing reconfigurability, deploying multi-task learning (MTL) algorithms on ONNs requires re-building and duplicating the physical diffractive systems, which significantly degrades the energy and cost efficiency in practical application scenarios. This work presents a novel ONNs architecture, namely, RubikONNs, which utilizes the physical properties of optical systems to encode multiple feed-forward functions by physically rotating the hardware similarly to rotating a Rubik's Cube. To optimize MTL performance on RubikONNs, two domain-specific physics-aware training algorithms RotAgg and RotSeq are proposed. Our experimental results demonstrate more than 4x improvements in energy and cost efficiency with marginal accuracy degradation compared to the state-of-the-art approaches.