Reaching devices on Subnets
Solution 1:
Your router 192.168.0.1 is responsible for routing this traffic since it is the common gateway between all of the subnets.
To route this traffic your router needs an IP in each of the respective subnets. Brandon Xavier is correct in saying this is device specific in how you can accomplish this.
The proper way to accomplish traffic segregation is through the use of VLans if your router supports this, you can then use your router to route the inter-vlan traffic.
VLAN 1 Router Interface = 192.168.0.1/24
VLAN 2 Router Interface = 192.168.2.1/24
VLAN 3 Router Interface = 192.168.3.1/24
All your devices should use the default gateway of their respective VLans.
Add routes to your router to route between the VLans accordingly.