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The deployment of Deep Learning Recommendation Models (DLRMs) involves the parallelization of extra-large embedding tables (EMTs) on multiple GPUs. Existing works overlook the input-dependent behavior of EMTs and parallelize them in a coarse-grained manner, resulting in unbalanced workload distribution and inter-GPU communication. To this end, we propose OPER, an algorithm-system co-design with OPtimality-guided Embedding table parallelization for large-scale Recommendation model training and inference. The core idea of OPER is to explore the connection between DLRM inputs and the efficiency of distributed EMTs, aiming to provide a near-optimal parallelization strategy for EMTs. Specifically, we conduct an in-depth analysis of various types of EMTs parallelism and propose a heuristic search algorithm to efficiently approximate an empirically near-optimal EMT parallelization. Furthermore, we implement a distributed shared memory-based system, which supports the lightweight but complex computation and communication pattern of fine-grained EMT parallelization, effectively converting theoretical improvements into real speedups. Extensive evaluation shows that OPER achieves 2.3× and 4.0× speedup on average in training and inference, respectively, over state-of-the-art DLRM frameworks.