I've searched the forums and found the commands and scripts to remove these files created by Mac but even logged on as root, I get Permission Denied.  How do I fix this?  What ls command option can I use to even see these files?

"ls -a" will show dot files.

This will remove all .Appledouble files:

 find / -name ".AppleDouble" -depth -exec rm -Rf {} \;

This will remove all .Appledouble files:

 find / -name ".AppleDouble" -depth -exec rm -Rf {} \;

 

This is the exact command I'm using but I'm getting "Permission Denied" on all of the files.  Logged on as root when I'm executing this.

Logged into the server or OS X?

Telnet'd into server from OSX terminal.

The files must be open. Turn off the share and retry.