Can I create a virtual internal network for my virtual machines in ESXi without using a physical nic?

Using ESXi 4.1

Want my Virtual Machines to be able to communicate with each other, share files, etc.

I have 2 nics that go from the server to the network (one public and one private) however these are real nics on real networks, can I create a virtual network that exists entirely within ESXi for the VMs to communicate so I don't need the nics at all?

Obviously I would still need the nics for connecting to anything else, but this should be possible for my VMs only right?

Yes, it is very easy to do this. Simply create a vSwitch that doesn't bridge to any real interfaces, then connect the VMs to that vSwitch. You'll need to handle IP assignments on your own though, since ESX(i) doesn't do all that silly DHCP/NAT funny business that the consumer versions do.