How to delete zero byte files

I have several files on my desktop that are greyed-out that I can't delete in any of the normal techniques. It doesn't affect performance (as far as I know), but is just annoying that they are there at all. The attributes are strange. (1) Creation date is 1969, December 31 at 16:00. (2) Sharing & Permissions list me (admin user) twice, and once indicates that I have "Custom" access (whatever that is). I cannot change or delete any of these attributes. I get an error message reading saying "Image xxx is in use by Mac OSX and can't be opened". What might be using it?

Any idea of how to get rid of these (or how they originated) would be appreciated.

Czet