Single image deraining is an important and challenging task for some downstream artificial intelligence applications such as video surveillance and self-driving systems. Most of the existing deep-learning-based methods constrain the network to generate derained images but few of them explore features from intermediate layers, different levels, and different modules which are beneficial for rain streaks removal. In this paper, we propose a high-order collaborative network with multi-scale compact constraints and a bidirectional scale-content similarity mining module to exploit features from deep networks externally and internally for rain streaks removal. Externally, we design a deraining framework with three sub-networks trained in a collaborative manner, where the bottom network transmits intermediate features to the middle network which also receives shallower rainy features from the top network and sends back features to the bottom network. Internally, we enforce multi-scale compact constraints on the intermediate layers of deep networks to learn useful features via a Laplacian pyramid. Further, we develop a bidirectional scale-content similarity mining module to explore features at different scales in a down-to-up and up-to-down manner. To improve the model performance on real-world images, we propose an online-update learning approach, which uses real-world rainy images to fine-tune the network and update the deraining results in a self-supervised manner. Extensive experiments demonstrate that our proposed method performs favorably against eleven state-of-the-art methods on five public synthetic datasets and one real-world dataset.