State estimation is a critical foundational module in robotics applications, where robustness and performance are paramount. Although in recent years, many works have been focusing on improving one of the most widely adopted state estimation methods, visual inertial odometry (VIO), by incorporating multiple cameras, these efforts predominantly address synchronous camera systems. Asynchronous cameras, which offer simpler hardware configurations and enhanced resilience, have been largely overlooked. To fill this gap, this paper presents VINS-Multi, a novel multi-camera-IMU state estimator for asynchronous cameras. The estimator comprises parallel front ends, a front end coordinator, and a back end optimization module capable of handling asynchronous input frames. It utilizes the frames effectively through a dynamic feature number allocation and a frame priority coordination strategy. The proposed estimator is integrated into a customized quadrotor platform and tested in multiple realistic and challenging scenarios to validate its practicality. Additionally, comprehensive benchmark results are provided to showcase the robustness and superior performance of the proposed estimator.