In real-world scenarios, it is desirable for embodied agents to have the ability to leverage human language to gain explicit or implicit knowledge for learning tasks. Despite recent progress, most previous approaches adopt simple low-level instructions as language inputs, which may not reflect natural human communication. It's not clear how to incorporate rich language use to facilitate task learning. To address this question, this paper studies different types of language inputs in facilitating reinforcement learning (RL) embodied agents. More specifically, we examine how different levels of language informativeness (i.e., feedback on past behaviors and future guidance) and diversity (i.e., variation of language expressions) impact agent learning and inference. Our empirical results based on four RL benchmarks demonstrate that agents trained with diverse and informative language feedback can achieve enhanced generalization and fast adaptation to new tasks. These findings highlight the pivotal role of language use in teaching embodied agents new tasks in an open world. Project website: https://github.com/sled-group/Teachable_RL