Quadrotors and multirotors in general are common in many inspection and surveillance applications. For these applications, visual-inertial odometry is a common way to localize the vehicles and observe the environment. However, unlike with wheeled mobile robots, quadrotor localization algorithms often do not use knowledge of the control inputs and the full vehicle dynamics as a process model for localization. Rather, they use kinematic models, with the IMU providing acceleration and angular velocity. One of the reasons for avoiding the use of dynamics is that, until recently quadrotor aerodynamic effects have not been considered in the literature and hence the dynamic models for quadrotors have been less accurate than those for wheeled mobile robots. The main aerodynamic terms that are significant are first-order effects that are linear in velocity and angular velocity. They are predominantly caused by aerodynamic interaction with the spinning propellers. This work investigates the models for such effects, as well as what can be gained if such aerodynamic effects are incorporated into the dynamic model and the full dynamics are used for state estimation. We develop novel IMU-based filters, the end results of which are used to estimate the wind velocity of the quadrotor or, indoors, when the ambient wind is zero, the velocity of the quadrotor. In addition, these filters estimate the many aerodynamic parameters in the model online. They may also be used to estimate sensor biases and inertial parameters. We demonstrate the effectiveness of these filters through experiments. We also present nonlinear observability analyses that theoretically determine the observability properties of the systems.