You have set up a class C network. Your network mask should be 255.255.0.0. Make sure all of your machines have that netmask and then reboot everything including the routers/switches.
If this does not work out-of-the-box, then you may have to set up a static route on those machines that you are having trouble with using route.
route add -net 220.127.116.11 netmask 255.255.255.0 dev eth0
adds a route to the local network 192.56.76.x via "eth0". The word "dev" can be omitted here.
So your command might be:
But you would only have to do that on machines that you are having trouble with connecting to your NAS.
sudo route add -net 192.168.20.0 netmask 255.255.0.0
For more complicated routing look at your dhcp server: https://help.ubuntu.com/community/isc-dhcp-server or https://help.ubuntu.com/community/dhcp3-server