My setup is main website server in one datacenter and mirrors in multiple other datacenters. I'd like to know what are my options to transfer traffic secure and stable between servers? Ssh tunneling or maybe stunnel or something else?
You probably want to use IPSEC in transport mode. Loosely related are discussions about opportunistic encryption. That term will give you many guides on implementation. Dropping the "fallback" part of those will provide you what you want.
You can do this node-to-node (each machine) or establish it between your routing choke points... probably at the edge routers.