Does the NAS box support NFS? If not it may support the cifs filesystem, which would allow you to use Linux permissions and acls.
The permissions on a vfat or ntfs filesystem doesn't support Linux permissions, and you need to set the permissions with how it is mounted. Either through the properties tag on the desktop icon, or by mounting it and including permissions with the mount.
sudo mount -t cifs //nas-device/share /mnt/mount_point -o rw,uid=<your_usernmame>,gid=<your_group>,fmask=0117,dmask=0007,utf8
If the device supports cifs, and a Linux filesystem like ext3 is used inside the device, then you can change permissions on files and directories, and even use setfacl & getfacl. If a windows filesystem is used and/or only smbfs is supported, then the uid,gid,fmask,dmask options are fallbacks and determine the permissions of the files and directories. For security reasons, don't set the 'x' bit for files on mass storage filesystems; but you need the 'x' bit for directories. Hence, fmask & dmask are used instead of simply umask.
You can also create an fstab entry and even be able to mount it as a normal user:
//nas-device/share /mnt/mount_point cifs rw,uid=<your_username>,gid=<your_group>,fmask=0117,dmask=0007,noauto,user,utf8
Running nmap to see which ports the NAS device has open will tell you if both windows smb (or cifs) and nfs are supported.
tarting Nmap 4.75 ( http://nmap.org ) at 2009-02-27 07:54 CST
Interesting ports on hpmedia.jesnet (192.168.1.104):
Not shown: 994 closed ports
PORT STATE SERVICE
22/tcp open ssh
111/tcp open rpcbind
139/tcp open netbios-ssn
445/tcp open microsoft-ds
2049/tcp open nfs
3306/tcp open mysql
Ports 111 & 2049 are used for NFS. Ports 139 & 445 are used by Samba/Windows.
Older 98 & 95 hosts used 137-139 & 445 for windows.
If you see ports 111 and 2049, then use NFS instead.