In this paper, we present a Radar-Inertial Odom-etry (RIO) framework capable of running on a portable resource-constrained embedded computer in real-time as a state estimator for closing the feedback control loop on an Unmanned Aerial Vehicle (UAV) platform. The presented framework ef-ficiently implements a RIO approach relying on the multi-state tightly-coupled Extended Kalman Filter (EKF) fusing instantaneous velocities of and distances to 3D points delivered by a lightweight, low-cost, off-the-shelf Frequency Modulated Continuous Wave (FMCW) radar with Inertial Measurement Unit (IMU) readings. The usage, accuracy and consistency of the implemented framework are improved compared to state-of-the-art by the online calibration of the sensors' extrinsic parameters. Our method is particularly relevant for (but not limited to) UAVs, enabling them to navigate autonomously in Global Navigation Satellite System (GNSS)-denied environments using very affordable and accessible hardware. In addition, thanks to the properties of the radar sensor, we enable autonomous navigation in challenging conditions for robot perception due to external factors such as fog, darkness or strong illumination which might be encountered in disaster zones. We show in real-world closed-loop flight experiments the effectiveness and efficiency of our estimator. The beneficial impact of the online calibration on estimation accuracy and consistency is also shown. Moreover, we compare the presented approach to a state-of-the-art vision-based algorithm (Visual-Inertial Odometry (VIO)) in visually degraded conditions.