Learning to adapt to a series of different goals in visual navigation is challenging. In this work, we present a model-embedded actor-critic architecture for the multigoal visual navigation task. To enhance the task cooperation in multigoal learning, we introduce two new designs to the reinforcement learning scheme':' inverse dynamics model (InvDM) and multigoal colearning (MgCl). Specifically, InvDM is proposed to capture the navigation-relevant association between state and goal and provide additional training signals to relieve the sparse reward issue. MgCl aims at improving the sample efficiency and supports the agent to learn from unintentional positive experiences. Besides, to further improve the scene generalization capability of the agent, we present an enhanced navigation model that consists of two self-supervised auxiliary task modules. The first module, which is named path closed-loop detection, helps to understand whether the state has been experienced. The second one, namely the state-target matching module, tries to figure out the difference between state and goal. Extensive results on the interactive platform AI2-THOR demonstrate that the agent trained with the proposed method converges faster than state-of-the-art methods while owning good generalization capability. The video demonstration is available at https://vsislab.github.io/mgvn.