In order to access a site via the bare domain without a port number in the URL, the service must be listening on port 80 (for HTTP) or 443 (for HTTPS). Only one service can be listen to a port at a time. So in order to do what you want, you’ll need to use a reverse proxy of some sort. Nginx is a good fit for this. Let it listen on port 80 and then direct the request to the appropriate service based on the domain name. Here’s a really basic example:

upstream app_server_one {
    server 127.0.0.1:2082 fail_timeout=0;
}

upstream app_server_two {
    server 127.0.0.1:2083 fail_timeout=0;
}

server {
    listen 80 default_server;
    listen [::]:80 default_server ipv6only=on;
    server_name abc.com;

    location / {
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header Host $http_host;
        proxy_redirect off;
        proxy_pass http://app_server;
    }
}

server {
    listen 80 default_server;
    listen [::]:80 default_server ipv6only=on;
    server_name def.com;

    location / {
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header Host $http_host;
        proxy_redirect off;
        proxy_pass http://app_server_two;
    }
}

Note that setting the server_name directive is important here.

For more info on Nginx, check out:

• How To Set Up Nginx Server Blocks (Virtual Hosts) on Ubuntu 14.04 LTS