What are the approaches to private computations?
If the VM actually has anything that needs protection, running the VM on untrusted hosts is not secure (period). There is nothing that will change that.  

Going to homomorphic encryptions etc. implies that even the VM doesn't know any secrets, only the source of the data (outside of VM and host) does. In this case, having a VM or not isn't even relevant.
There are of course still problems with the authenticity of the results etc. - just encrypting is never enough.  

Using Intel SGX from within VMs relies on the support/cooperation of the VM software - meaning, it might be useful for separating VMs fom each other, but it can not help VMS against their malicious host.
Given that VMs are, well, virtualized, any hardware support is useless in your scenario. If the host and the virtualization software can't be trusted, your VM is not secure.