Adversarial training is an important topic in robust deep learning, but the community lacks attention to its practical usage. In this paper, we aim to resolve a real-world challenge, i.e., training a model on an imbalanced and noisy dataset to achieve high clean accuracy and adversarial robustness, with our proposed Omnipotent Adversarial Training (OAT) strategy. OAT consists of two innovative methodologies to address the imperfection in the training set. We first introduce an oracle into the adversarial training process to help the model learn a correct data-label conditional distribution. This carefully-designed oracle can provide correct label annotations for adversarial training. We further propose logits adjustment adversarial training to overcome the data imbalance issue, which can help the model learn a Bayes-optimal distribution. Our comprehensive evaluation results show that OAT outperforms other baselines by more than 20% clean accuracy improvement and 10% robust accuracy improvement under complex combinations of data imbalance and label noise scenarios. The code can be found in https://github.com/GuanlinLee/OAT.