If you want to run it "without a port" like you describe, you're actually going to be running it on port 80. You can't do this without root permissions.
So instead of
node server.js
You need
sudo node server.js
This is assuming you have sudo permissions on the machine you're trying to run it on. Otherwise you're going to run into EACCESS problems. That's what sarnold is trying to tell you.