Cannot access full site except from WAN

I had setup an installation of WP for testing on my Ubuntu machine at home to later be installed on another server at another house for a very specific blogging site that cannot effectively run on a traditional hosting site.
Following every instruction I could find on installing WP, I had installed WP in my, Ubuntu box in my house, in the /var/www/ folder and then ran the install by opening Firefox and opening https://localhost. Ran through the install queries providing the DB info and the site got installed without a hitch except for when I tried to access the site from another machine in the house or from outside my LAN, all I would get was a the Index page in HTML, not PHP, and clicking on any of the links would get a Bad request error 400. There after I wiped out the database and overwrote the folders in the /var/www/ folder with the default WP install and proceeded to run the install from Outside my LAN. So now the site can Only be seen from outside my house but any attempts to see the site from my LAN or from my machine ends up with the index page in HTML and clicking a Link on the page I get Bad request error 400.
I had found a Workaround where the machines on the LAN wold have their Hosts file edited to point to the IP of the host server in the house or in the case of my Ubuntu Box, to point to Localhost when my.site.com is used in the browser.
What I would like to know is how to setup this server so that it can be accessed both from my LAN and from the WAn without having to manipulate the Hosts file in either Linux or Windows. Why is it that ‘phpmyadmin’ can be accessed in a browser on my local machine, another machine on the LAN or from the WAN, yet the WP site will only work with the URL that is in WordPress Address (URL) or Site Address (URL) but not work dynamically.

Please Help.