Hi again.
Removing the disks from the VDP worked for the "fourth" server mentioned earlier and I'm now able to take backups of that one again.
The other three however still fails when attempting to back them up. Looking in the logs in \usr\local\avamarclient\var-proxy-N\jobname.vmimagew.log I see this message:
"Too many extra snapshot files (1) were found on this Windows VMs datastore. This can cause a problem for the backup or restore"
I tried to take new snapshots and do a "Delete all" again as you recommended but I still get the same error. (No shapshots are visible any more on the VMs in the VMWare client)
Any thoughts on how fix this as well? 
Best regards