I think one big reason I dislike reading on screens is the fact that I am basically shining a flashlight in my eyes for hours.
With software, this is less of a problem for two reasons: First off, the visual scheme is designed for a monitor (and not designed for paper but shown on a monitor like with books or articles). Second, the image is very dynamic, so paper isn't an alternative anyhow.
The first thing to try is to turn down the brightness of your monitor. This may seem to make it very dark at first, but backlight is different from contrast. I find that I easily get used to the lowest brightness setting on my monitors after an hour or so. If the wall or desk space behind your computer is dark, you may also want to put a weak desk lamp so that it shines behind your monitor and reduces the contrast of the wall vs. your screen.
If you do a lot of reading, you should consider rotating your monitor (most newer mounts support this) to have it oriented in portrait instead of landscape.
F.lux was already mentioned, and it can be very helpful, but I think it's more to do with effects of using a computer at late hours at home. At noon, a f.lux filtered screen will look about the same as without a filter anyway. If you are lucky enough to have a fancy monitor, you might even find sophisticated software to control contrast and brightness.
I have had a much better experience reading books on a Kindle. Because the screen is not backlighted, but instead gets illuminated by ambient lighting, it is much less irritating. Unfortunately the PDF support of Kindles isn't very good, you must scroll through each page as if it was a picture, and for papers which have small type, multiple columns and frequently refer to figures on other pages, the Kindle's interface will dirve you crazy. Kindle DX has a larger screen, about 8", though still not as big as a paper.
An alternative is, if you can find an HTML version of your article, to read that in your Kindle using the Web Browser.
Since you are stuck on a computer, I would recommend reading in a software such as Foxit Reader, which have very nice tools for highlighting and annotating. You could even invest in a drawing tablet such as Wacom to help you draw on figures and so on.
IMO this is a lost cause and you should print articles. You have read books and papers from actual paper for decades of your life, including in childhood. Your brain and your eyes are probably accustomed to it much better, and there might be psychological cues which help you focus (not to mention distraction on the computer like email, software popups and so on).
The paper consumption can be quite big, but honestly, how many "more important" uses for paper are there besides scientific research? In any case;
- You can use low-grade, recycled paper
- You can print on both sides, or reuse single-side paper as scratch paper
- You can recycle your own papers after you read them
- Only print papers that you actually want to read, instead of skim for 5 minutes (this should consume a very small amount of paper compared to your other daily activities)
Like you say, it's easy to end up with a huge mess. But that's a question of being organized. If you are a little proactive and develop a reasonable filing system (even a few manilla folders with labeled tabs can do wonders), you can keep the vast majority of the clutter under control very easily.