Deep reinforcement learning is confronted with problems of sampling inefficiency and poor task migration capability. Meta-reinforcement learning (meta-RL) enables meta-learners to utilize the task-solving skills trained on similar tasks and quickly adapt to new tasks. However, meta-RL methods lack enough queries toward the relationship between task-agnostic exploitation of data and task-related knowledge introduced by latent context, limiting their effectiveness and generalization ability. In this article, we develop an algorithm for off-policy meta-RL that can provide the meta-learners with self-oriented cognition toward how they adapt to the family of tasks. In our approach, we perform dynamic task-adaptiveness distillation to describe how the meta-learners adjust the exploration strategy in the meta-training process. Our approach also enables the meta-learners to balance the influence of task-agnostic self-oriented adaption and task-related information through latent context reorganization. In our experiments, our method achieves 10%-20% higher asymptotic reward than probabilistic embeddings for actor-critic RL (PEARL).