Achilleas,
I have just tested your sample data in ArcGIS Explorer 1500 (due out very soon) and it appears to display in the correct position (as far as I can tell).
Here are the steps I took:
1. Open ArcGIS Explorer
2. Set the Basemap to Bing Aerial imagery
3. Click the Explorer button/pearl in top left corner
4. Choose Map Properties
5. Select 2D Coordinate system tab
6. Pick �??Greek_Grid�?� from the drop down (via <More...> option)
7. In the Geographic Transformations box choose GGRS_1987_To_WGS_1984
8. Click OK
9. Click Add Content > Raster Data...
10. Browse for �??n.gonia_sdian63_58apo1.tif�?�
11. Click Open
12. This looks OK to me?
Regards
Mike