I have a provider hosted App and need to use modals in my App Pages. Is it possible to use SP Modal Dialogs from SP.UI.Dialog.js ?
What JS files are required to be included?
Never done it myself but I don't see any reason for why it can't done.
This sample shows how to build user interfaces in SharePoint-hosted apps that use the callout and dialog controls.
Check this out,
SharePoint 2013: Use list views, callouts, and dialogs in SharePoint-hosted apps
I don't have SharePoint 2013 component installed but if you look at solution provided in link in Default.aspx page you will find reference to this which means you can use it in apps.
<script type="text/javascript" src="/_layouts/15/sp.ui.dialog.js"></script> Edit
It's not possible, you might be able to trick SharePoint but then you will need to make changes to host web as described in this post.