Just in case you can't access QGIS, I've created three separate shapefiles and put them on dropbox.  The projection of these shapefiles is EPSG:4326

https://dl.dropboxusercontent.com/u/71658964/miconesia.zip

I used ogrinfo on the original file and it tells me the projection is EPSG:4326, I think, for example:

    ogrinfo -so FSM_adm_SBOC_PCRAFI.gdb state

    Had to open data source read-only.
    INFO: Open of `FSM_adm_SBOC_PCRAFI.gdb'
          using driver `OpenFileGDB' successful.
    
    Layer name: State
    Geometry: Multi Polygon
    Feature Count: 4
    Extent: (137.491872, 1.022685) - (163.051392, 10.036174)
    Layer SRS WKT:
    GEOGCS["GCS_WGS_1984",
        DATUM["WGS_1984",
            SPHEROID["WGS_84",6378137.0,298.257223563]],
        PRIMEM["Greenwich",0.0],
        UNIT["Degree",0.0174532925199433]]
    FID Column = OBJECTID
    Geometry Column = Shape
    SID: Real (0.0)
    State: String (0.0)
    Census_00: Real (0.0)
    Proj_10: Real (0.0)
    Shape_Length: Real (0.0)
    Shape_Area: Real (0.0)


Looking at your backdrop, I can see it has come from Google Maps.  So you will probably want to convert the shapefiles to EPSG:3857 - WGS84 / Pseudo Mercator, or just save the file geodatabase to a shapefile in that CRS.


Another dataset you may also be interested in is the WMS service [GSJ CCOP Combined Bedrock and Superficial Geology and Age](https://gbank.gsj.jp/ows/GSJ_CCOP_Combined_Bedrock_and_Superficial_Geology_and_Age/wms?)