If you want to sort this out using Terminal then do this:
Once Terminal is open type:
(without the $ obviously)
then
If your desktop files show up then you're in the right place. This is also a good time to check that the .DS_Store file is there also.
Then
When you're prompted hit 'y'
Close Terminal, logout then log back in. OS X will rebuild the .DS_Store file and hopefully if that is the issue then the icons should stop moving about.