What to do if you don't want to load JS files on mobile devices
The easiest (probably only realistic) way would be to create a second, javascript-less theme, and use the ThemeKey module to show that theme to mobile users based on user agent string. It's not exactly a foolproof method but then device-sniffing never is. 

The other option would be to write some javascript which responds to the Omega media query change event, and hooks/unhooks all other javascript events on the page based on the current device size. I can imagine that being very difficult to manage though.

The proper solution would be to design the theme in a mobile-first manner, building up the javascript functionality as you go and managing how it reacts to different breakpoints at an earlier stage. 

Removing all javascript for mobile devices means your users will be experiencing a site like they would have 10 years ago, with no UI richness. These days people expect more than that, especially since their devices can easily handle javascript/