Mass file+folder+directory move

Yes you can do this if you have a system where both the src files are accessible and the NAS. There are several ways to do this with a single command, but the tool rsync is probably the best one to go with:

$ sudo rsync -avz src /mnt/NAS/

The switches (from the rsync man page):

-a, --archive               archive mode; equals -rlptgoD (no -H,-A,-X)
-v, --verbose               increase verbosity
-z, --compress              compress file data during the transfer

So the -a switch is actually a macro for a whole bunt of switches:

-r, --recursive             recurse into directories
-l, --links                 copy symlinks as symlinks
-p, --perms                 preserve permissions
-t, --times                 preserve modification times
-g, --group                 preserve group
-o, --owner                 preserve owner (super-user only)
-D                          same as --devices --specials

Running as root

You'll want to run this as root to preserve the permissions and ownerships of the files + directories. Also this particular root user will need access to the NAS. This is sometimes not setup by default so you may need the help of an admin if you're not the one.

Before you get started

Typically you'll want to do some upfront analysis on the directories in question to see if there are any symbolic links or fifo type files. These will require additional switches to rsync so that it recreates them correctly in the target directory.

No direct mounting access to NAS

All is not lost if you can't directly mount the NAS on the same box where you have access to the src files. You can also rsync over ssh.

$ sudo rsync -avz src root@remoteserver:/mnt/NAS/.

There are more advanced options if neither of these suite your needs.