Certain configurations of removable oral devices are described. In some instances, the removable oral device includes a palatal element. In certain configurations, the palatal element may comprise a variable hardness at different areas, e.g., edges can be softer than other areas of the removable oral device. In other instances, the removable oral device may comprise two or more individual palatal elements which together can form the palatal element and permit user adjustment of the oral volume. Various materials used in the palatal element are described. Sensors and other on-board devices are also described.