Recently, quadrotors are gaining significant attention in aerial transportation and delivery. In these scenarios, an accurate estimation of the external force is as essential as the 6 degree-of-freedom (DoF) pose since it is of vital importance for planning and control of the vehicle. To this end, we propose a tightly-coupled Visual-Inertial-Dynamics (VID) system that simultaneously estimates the external force applied to the quadrotor along with the 6 DoF pose. Our method builds on the state-of-the-art optimization-based Visual-Inertial system, with a novel deduction of the dynamics and external force factor extended from VIMO. Utilizing the proposed dynamics and external force factor, our estimator robustly and accurately estimates the external force even when it varies widely. Moreover, since we explicitly consider the influence of the external force, when compared with VIMO and VINS-Mono, our method shows comparable and superior pose accuracy, even when the external force ranges from neglectable to significant. The robustness and effectiveness of the proposed method are validated by extensive real-world experiments and application scenario simulation. We will release an open-source package of this method along with datasets with ground truth force measurements for the reference of the community.