Learning-based inertial odometry has achieved remarkable progress in pedestrian navigation. However, extending these methods to quadruped robots remains challenging due to their distinct and highly dynamic motion patterns. Models that perform well on pedestrian data often experience severe degradation when deployed on legged platforms. To tackle this challenge, we introduce X-IONet, a cross-platform inertial odometry framework that operates solely using a single Inertial Measurement Unit (IMU). X-IONet incorporates a rule-based expert selection module to classify motion platforms and route IMU sequences to platform-specific expert networks. The displacement prediction network features a dual-stage attention architecture that jointly models long-range temporal dependencies and inter-axis correlations, enabling accurate motion representation. It outputs both displacement and associated uncertainty, which are further fused through an Extended Kalman Filter (EKF) for robust state estimation. Extensive experiments on the public RoNIN pedestrian dataset, the GrandTour quadruped dataset, and a self-collected Go2 quadruped dataset demonstrate that X-IONet achieves state-of-the-art performance, reducing ATE and RTE by 14.3% and 11.4% on RoNIN, 11.8% and 9.7% on GrandTour, and 52.8% and 41.3% on Go2. These results highlight X-IONet's effectiveness for accurate and robust inertial navigation across both human and legged robot platforms.