Here's the short demo of just few possible settings for DJ-ImageSlider.
Using the advanced module settings you can set it to work as you need it to.
We used free Joomla template from Joomla-Monster in this demo site.
Once you open it on your mobile device you'll notice the DJ-ImageSlider fitting to your device. There's also DJ-Menu used that changes to select list on mobile devices.
You can also check responsiveness of that template and extensions clicking this responsive joomla template demo link.