Those commands use absolute paths. If they fail, it means your disk isn't mounted as /mnt/sda1 - you will have to figure out its mount point through "ls /mnt".
If it uses a volume name instead of a device name, then it means it's not formatted as ext2/ext3.
Here's the result of my "mount" command:
admin@RT-N66U:/# mount
rootfs on / type rootfs (rw)
/dev/root on / type squashfs (ro)
proc on /proc type proc (rw)
tmpfs on /tmp type tmpfs (rw)
devfs on /dev type tmpfs (rw,noatime)
sysfs on /sys type sysfs (rw)
devpts on /dev/pts type devpts (rw)
/dev/mtdblock4 on /jffs type jffs2 (rw,noatime)
usbfs on /proc/bus/usb type usbfs (rw)
/dev/sda1 on /tmp/mnt/optware type ext3 (rw,nodev,noatime,data=ordered)
admin@RT-N66U:/#
As you can see my disk is ext3 formatted
and that is the reult of a cd /mnt/sda1/Torrent command:
admin@RT-N66U:/# cd /mnt/sda1/Torrent
-sh: cd: can't cd to /mnt/sda1/Torrent
admin@RT-N66U:/#
While this is the result of an ls -l /tmp/mnt/optware command
admin@RT-N66U:/# ls -l tmp/mnt/optware
drwxrwxrwx 8 admin root 4096 Jan 1 2011 Download2
drwxrwxrwx 6 admin root 4096 Jan 6 04:54 Torrent
drwxr-xr-x 11 admin root 4096 Dec 10 13:18 asusware
drwx------ 2 admin root 16384 Mar 3 2012 lost+found
-rw-rw-rw- 1 admin root 222 Jan 1 2011 port_trigger_list.txt
-rw-rw-rw- 1 admin root 0 Oct 1 01:47 static_dhcp_list.txt
admin@RT-N66U:/#
Of course the Download2 directory is now useless and almost empty.
Now I'm curious to know which is the mechanism that allows to address through the partition's name.
A strange behavior I noticed, but I guess related to the version of transmission and not to it's entware implementation, is that when I tried to rebuild my seed tree, after copying my files to the download dir and the torrents in the torrents dir (I had to change the /asusware/etc/transmission/torrents permissions to do so) and then started transmission, the program did not start to verify the downloads: I had toi force manually the verify process to avoid redownloading everything.