You can not use cloudlinux on the physical server if are going to virtulize it but you can definitely use it on the VPS server. A cloudlinux is ideal for shared servers as it would limit resources per users thus offering equal amount of resources to every user and in case any user crosses your defined limit he would receive an error.
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Keep in mind every vm will have to have a Cloudlinux licensing. If the vps itself is not being used as a shared server it is honestly a waste to have Cloudlinux installed.
If you want to host any VPSes (even just 1!) your dedicated server becomes a VPS node. If you want to host websites too, you will need to create a VPS on your node and use that as your hosting platform. For your node, you can use hypervisor software (XenServer or VMWare ESX) or Xen on top of something like CentOS. For your hosting VPS, cloud linux would work. You can't use Virtuozzo as your node software since it doesn't allow for compilation of custom kernel modules, like net said.