Oh gods.
In theory: simply migrate the containers to the new machine. Change the IPs in Virtuozzo. Reconfigure Plesk to use the new IPs. Done.
In practice: Manually copy OS template cache to new machine. Read all the posts in the Parallels forum regarding this. There are several important threads -- one about how to prepare and one about what to do when it goes wrong. Do a test migration. Check template consistency. Fix problems. Try again. Also Read all Parallels KBs relating to migration.
http://kb.parallels.com/en/113129
http://kb.parallels.com/en/114232
And if you are going from an older version to 4.7, expect problems with memory configuration - be ready to change to vswap and remove all the old UBC/SLM configuration parameters.
Now in my case I had no problems with the "in theory". It worked, sort of. But then the new memory management system nearly killed me until I discovered that I should really wipe the configuration and start from scratch. Also check out vm_overcommit setting.
Then I found that loads of OS template cache files had not been migrated. They were for older versions of files that had long since been overwritten, but which were still referenced by the container. No harm done but it was annoying. Also some older OSes may no longer have their files in the same places that the OS template expects them to be (Older Ubuntu, Older Debian, and of course things like Centos 4 are not there anymore). VZ is supposed to copy the needed files from the source host node if they aren't on the destination, but doesn't (at least not always). The result can be a mess.
Bottom line -- post on the Parallels forum about this. There are more people there who can help you. And make sure you take a full copy of your OS template cache along to your new server.