To fill it you would have to stretch it or transcode it to something that works. Some transcoders can set the video to a specific X by Y size so that could fix these but no setting has been acceptable to those that asked your question to date.
I am using VLC as a video playlist to export to a secondary monitor. I have noticed a small .mov file plays excellent and fills the screen. The larger .avi files do not fill the screen and have a green border either on side and bottom or just right side depending on ratio settings. Is it possible to get an .avi to fill the screen.

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic