I'm wondering if it is possible to setup NGIX in a way, where I could get access to any port (ex: 80) for any VM or server inside local network by using it's IP as part of a URL.

So let's say if my public IP is 111.111.111.111 and I have a webserver at home with a local ip 192.168.1.5, I could access the port 80 by typing:

http://111.111.111.111/192.168.1.5
or
http://111.111.111.111/192_168_1_5

Use a local DNS (or hosts file).

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nginx for Windows http://nginx-win.ecsds.eu/

What is keeping you from having a location with a pattern parsing {localip}[/{localpath}] and proxy that to http://{localip}/{localpath}?

If your NGINX is reachable on its public IP address, but actually runs in a private IP address range inside your local network, you only have to make sure that nobody has the glorious idea of specifying the NGINX local IP address as a proxy destination.

--j.