In recent years, the subject of deep reinforcement learning (DRL) has developed very rapidly, and is now applied in various fields, such as decision making and control tasks. However, artificial agents trained with RL algorithms require great amounts of training data, unlike humans that are able to learn new skills from very few examples. The concept of meta-reinforcement learning (meta-RL) has been recently proposed to enable agents to learn similar but new skills from a small amount of experience by leveraging a set of tasks with a shared structure. Due to the task representation learning strategy with few-shot adaptation, most recent work is limited to narrow task distributions and stationary environments, where tasks do not change within episodes. In this work, we address those limitations and introduce a training strategy that is applicable to non-stationary environments, as well as a task representation based on Gaussian mixture models to model clustered task distributions. We evaluate our method on several continuous robotic control benchmarks. Compared with state-of-the-art literature that is only applicable to stationary environments with few-shot adaption, our algorithm first achieves competitive asymptotic performance and superior sample efficiency in stationary environments with zero-shot adaption. Second, our algorithm learns to perform successfully in non-stationary settings as well as a continual learning setting, while learning well-structured task representations. Last, our algorithm learns basic distinct behaviors and well-structured task representations in task distributions with multiple qualitatively distinct tasks.