In recent years, LiDAR-based localization and mapping methods have achieved significant progress thanks to their reliable and real-time localization capability. Considering single LiDAR odometry often faces hardware failures and degradation in practical scenarios, Multi-LiDAR Odometry (MLO), as an emerging technology, is studied to enhance the performance of LiDAR-based localization and mapping systems. However, MLO can suffer from high computational complexity introduced by dense point clouds that are fused from multiple LiDARs, and the continuous-time measurement characteristic is constantly neglected by existing LiDAR odometry. This motivates us to develop a Continuous-Time and Efficient MLO, namely CTE-MLO, which can achieve accurate and real-time state estimation using multi-LiDAR measurements through a continuous-time perspective. In this paper, the Gaussian process estimation is naturally combined with the Kalman filter, which enables each LiDAR point in a point stream to query the corresponding continuous-time trajectory within its time instants. A decentralized multi-LiDAR synchronization scheme also be devised to combine points from separate LiDARs into a single point cloud without the requirement for primary LiDAR assignment. Moreover, with the aim of improving the real-time performance of MLO without sacrificing robustness, a point cloud sampling strategy is designed with the consideration of localizability. The effectiveness of the proposed method is demonstrated through various scenarios, including public datasets and real-world autonomous driving experiments. The results demonstrate that the proposed CTE-MLO can achieve high-accuracy continuous-time state estimations in real-time and is demonstratively competitive compared to other state-of-the-art methods.