So, this means I can manage my 4.0 & 4.1 hosts using vCenter 5.1, is that right?
Yes, you may managed the hosts, using vCenter 5.1
vMotion is an ideal solution but can I manage one Datastores on both 4.x and 5.x? I heard that it's not advised to allow same Datastore (Volume) managed by two different versions of vSphere! Is that true? If so, then how can I move VM's? Unregistring from 4.x and move the VM files and re-regestring in 5.x and select Move?
Yes, you may managed one datastore on both Hosts, but make sure that your datastore is running on VMFS3 not VMFS5, If VMFS5 the datastore not visible on the host 4.x , You may lack of VMFS5 functionality/capatibility when still using VMFS3 on version 5 host.
If you are using different cluster, you may used the vMotion to move from 4.x to 5.x., not required to un registering from 4.x to 5.x