Check each application you run from a second account created in Apple menu -> System Preferences -> Accounts to see if any creates those files.
If not, and there is no software that could logically write those files to your desktop, backup you data first, and then try deleting them. Sometimes these files might be locked, in which case you might need to use Secure Empty Trash from the menu which has Empty Trash, or even my software.
http://www.macmaps.com/backup.html
explains various means of backing up your data in case some of those files prove to be important for something and you need them back. And here is the link for my Force Empty Trash program:
http://www.macmaps.com/software.html
Disclaimer: Reference to links I make to my Macmaps.com website are a for your information only type reference. I do not get any profit from this page, and it is open to the public.