Optical neuromorphic computing has demonstrated promising performance with ultra-high computation speed, high bandwidth, and low energy consumption. The traditional optical neural network (ONN) architectures realize neuromorphic computing via electrical weight encoding. However, previous ONN design methodologies can only handle static linear projection with stationary synaptic weights, thus fail to support efficient and flexible computing when both operands are dynamically-encoded light signals. In this work, we propose a novel ONN engine O²NN based on wavelength-division multiplexing and differential detection to enable high-performance, robust, and versatile photonic neural computing with both light operands. Balanced optical weights and augmented quantization are introduced to enhance the representability and efficiency of our architecture. Static and dynamic variations are discussed in detail with a knowledge-distillation-based solution given for robustness improvement. Discussions on hardware cost and efficiency are provided for a comprehensive comparison with prior work. Simulation and experimental results show that the proposed ONN architecture provides flexible, efficient, and robust support for high-performance photonic neural computing with fully-optical operands under low-bit quantization and practical variations.