This study proposes a real-time LiDAR-based approach for efficient path following in omni-wheeled robots (OWRs) capable of dynamically adapting to surrounding obstacles. To achieve this, two fuzzy control schemes are developed: Fuzzy Sliding-Mode Tracking Control (FTC) for precise path following and Fuzzy Obstacle-avoidance Control (FOC) for real-time collision avoidance using LiDAR data. FTC utilizes fuzzified sliding surfaces, derived from tracking errors, to follow a planned path. In the presence of obstacles along the path, FOC, employing LiDAR measurements, assesses collision distance and direction, ensuring safe navigation. The outputs of FTC and FOC are seamlessly merged using a smooth switching factor to generate voltage inputs for the actuators. The effectiveness of the proposed approach is demonstrated through extensive simulations and real-world experiments under various conditions, including wheel disturbances, diverse trajectories, and varying initial positions.