This paper explores traversability estimation for robot navigation. A key bottleneck in traversability estimation lies in efficiently achieving reliable and robust predictions while accurately encoding both geometric and semantic information across diverse environments. We introduce Navigation via Mixture of Experts (NAVMOE), a hierarchical and modular approach for traversability estimation and local navigation. NAVMOE combines multiple specialized models for specific terrain types, each of which can be either a classical model-based or a learning-based approach that predicts traversability for specific terrain types. NAVMOE dynamically weights the contributions of different models based on the input environment through a gating network. Overall, our approach offers three advantages: First, NAVMOE enables traversability estimation to adaptively leverage specialized approaches for different terrains, which enhances generalization across diverse and unseen environments. Second, our approach significantly improves efficiency with negligible cost of solution quality by introducing a training-free lazy gating mechanism, which is designed to minimize the number of activated experts during inference. Third, our approach uses a two-stage training strategy that enables the training for the gating networks within the hybrid MoE method that contains nondifferentiable modules. Extensive experiments show that NAVMOE delivers a better efficiency and performance balance than any individual expert or full ensemble across different domains, improving cross-domain generalization and reducing average computational cost by 81.2% via lazy gating, with less than a 2% loss in path quality.