Currently, human-bot symbiosis dialog systems, e.g., pre- and after-sales in E-commerce, are ubiquitous, and the dialog routing component is essential to improve the overall efficiency, reduce human resource cost, and enhance user experience. Although most existing methods can fulfil this requirement, they can only model single-source dialog data and cannot effectively capture the underlying knowledge of relations among data and subtasks. In this paper, we investigate this important problem by thoroughly mining both the data-to-task and task-to-task knowledge among various kinds of dialog data. To achieve the above targets, we propose a Gated Mechanism enhanced Multi-task Model (G3M), specifically including a novel dialog encoder and two tailored gated mechanism modules. The proposed method can play the role of hierarchical information filtering and is non-invasive to existing dialog systems. Based on two datasets collected from real world applications, extensive experimental results demonstrate the effectiveness of our method, which achieves the state-of-the-art performance by improving 8.7\%/11.8\% on RMSE metric and 2.2\%/4.4\% on F1 metric.