Do radiologists read films online now or on those boxes?

Digital. Just like typewriters and CD's the film box is a thing of the past. Radiology is almost exlusively by computer in the US.
Both, mostly digital. We an read online or on viewboxes. Mostly digital these days - can be local networks or via the internet/"cloud.".
Mostly online. Most radiologic examinations - plain x-ray, ct scan, MRI scan - are done digitally and the output can be seen on a video screen without the need to expose or process film. This is more efficient, saves resources and can be easily transmitted to other parts of the country or the world.