On-Demand Routing (ODR) is one of the few simple routing methods. It is not a protocol by itself as it uses Cisco Discovery Protocol (CDP) to gather and propagate the route information.
ODR is designed for Hub-spoke networks, where the spokes are stub networks with nothing connecting them. As ODR is not a protocol to propagate routes to different routers.
Enabling ODR in the HUB router, the HUB router will install a default route into each Spoke router. This will eliminate the need for manual static route in each spoke router. The Spoke routers will send the prefixes to the HUB router. Prefixes insure that these routes are Variable Length Subnet Mask (VLSM). Furthermore, ODR routes can be redistributed into dynamic IP protocols.
For the above diagram. the required configuration would be
R2(config)#router ospf 1
R2(config)#redistribute odr subnets
It really is straight forward. Hope this was informative.