There are various front-ends for permission management, including right-clicking on a file or directory and selecting "Properties".
But it would be better to understand how Unix file permissions work, because what you are attempting to do is one thing, while what you THINK you are trying to do is another.
You do not want to assign "no user" to your files, you want to assign a single group to them, and then you want to ensure that that group has permission to read and write those files.
If `ls -l` shows drwxrwxrwx (777) permissions, then your current user and its current group, and all others, have full permission to the files. So that's very permissive and in theory you should have no problem there. But since you are, I am guessing that either the directory they are housed in has more restrictive permissions, or else you have some configuration issue in the way you are accessing the NAS over your network.
What are the permissions of the directory? and how are you accessing the NAS?