three.js can import all three formats although the support for FBX is a bit limited. Once loaded you can export to glTF and OBJ via GLTFExporter and OBJExporter however there is no FBXExporter. Supporting FBX is tricky since the format is complex and there is no real specification.
I’m not aware of a single tool that can do what you are looking for. However, there are projects for single conversion tasks like converting OBJ to glTF (GitHub - CesiumGS/obj2gltf: Convert OBJ assets to glTF) or FBX to glTF (GitHub - facebookincubator/FBX2glTF: A command-line tool for the conversion of 3D model assets on the FBX file format to the glTF file format.).