node.js: route request to different port on same host

You probably better use Nginx setting up a reverse proxy with different locations per application.

It's not what you ask for because it does not use node.js, but if it's the only purpose, Nginx really suits your needs.

For example a Nginx configuration file like should work the way you want :

server {
    listen 80;

    server_name myapp.com;

    location /app1 {
        proxy_pass http://APP_PRIVATE_IP_ADDRESS:3000;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection 'upgrade';
        proxy_set_header Host $host;
        proxy_cache_bypass $http_upgrade;
    } 

    location /app2 {
        proxy_pass http://APP_PRIVATE_IP_ADDRESS:3001;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection 'upgrade';
        proxy_set_header Host $host;
        proxy_cache_bypass $http_upgrade;
    } 

    location /app3 {
        proxy_pass http://APP_PRIVATE_IP_ADDRESS:3003;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection 'upgrade';
        proxy_set_header Host $host;
        proxy_cache_bypass $http_upgrade;
    } 
}

If you use express, you can try to create the app with the cli express application generator.

It creates an express app and returns it with module exports.

In the server.js file it pass to listen function of the server instance the express app object.

You can create more server object and listen different app with different port.

var server = http.createServer(app);
server.listen(port);
var server2 = http.createServer(app2);
server2.listen(port2);

If you want to point different app based on the url, you can instance an express router instead of express object.

var app1 = express.Router();

Then you can set all your routes into this object with classic get or post or other methods.

Now you are able to pass the router as a middleware of your main express app.

app.use( "app1/", app1 );

You can also pass an express app to middleware, instead of router object, in order to gain the possibility of exec the app with a different url and port server listening.