Java Open Street Map (JOSM) Editor

Java Open Street Map Editor (JOSM) is much more powerful than iD, Potlatch and other online editors. JOSM editor allows offline editing. You first select an area that you want to edit. Download the selected area and then start editing. Since internet connection is not required, editing is faster. 

Android Apps for OSM editing 

There are mainly two apps used in OSM editing OsmAnd and Vespucci. OsmAnd is an offline navigation app with voice guidance. It is not a complete OSM editor, but one can add and upload POI’s. Vespucci is a fullfledge OSM editor. It works like JOSM