The fusion scheme is crucial to the multi-sensor fusion method that is the promising solution to the state estimation in complex and extreme environments like underground mines and planetary surfaces. In this work, a light-weight iEKF-based LiDAR-inertial odometry system is presented, which utilizes a degeneration-aware and modular sensor-fusion pipeline that takes both LiDAR points and relative pose from another odometry as the measurement in the update process only when degeneration is detected. Both the CRLB theory and simulation test are used to demonstrate the higher accuracy of our method compared to methods using a single observation. Furthermore, the proposed system is evaluated in perceptually challenging datasets against various state-of-the-art sensor-fusion methods. The results show that the proposed system achieves realtime and high estimation accuracy performance despite the challenging environment and poor observations.