I've used screen with scientific applications, mainly R and SAS, for many years - I haven't touched IDL since graduate school but screen will run IDL fine.
Basically, open a terminal, run screen, then run IDL inside the screen session, and start your job. You can now disconnect and reconnect later, including reconnecting from home.
If all you want to do is look at plots, for R I use built-in terminal graphics (which works fine with screen after fiddling), for other things, I typically write out a png and view it with a web browser.
For X11 applications, you may find xpra of use -
https://github.com/Xpra-org/xpra - note that desktop linux is generally speaking moving away from X11 though, and you may be happier with a virtual desktop instead. Figuring out how to get Xpra working correctly might take too long to be worth the effort.