Is there any canon information on how Professor Binns is able to keep up with books/papers or grade student's home works? As a ghost - he shouldn't be able to use spells even if he is unable to physically touch stuff. It has been suggested on wikia that he used students to grade the papers for him. But what about end of year exams, OWLS or NEWTS?
While I give no credence to the wikia, in addition to what Richard has outlined, in Chamber of Secrets Professor Binns is able to open his notes without assistance:
Today was as boring as ever. Professor Binns opened his notes and began to read in a flat drone like an old vacuum cleaner until nearly everyone in the class was in a deep stupor, occasionally coming round long enough to copy down a name or date, then falling asleep again. He had been speaking for half an hour when something happened that had never happened before. Hermione put up her hand.
Chamber of Secrets - page 113 - Bloomsbury - chapter nine, The Writing On the Wall
If Professor Binns is able to handle his notes by opening them up -- I imagine he opened up a folder of some sort -- I don't see why he wouldn't be able to open a book and turn the pages. Accordingly, Professor Binns would just go about his daily business as any non-ghost would -- this is how he would get things done.
In Chamber of Secrets, chapter eight, The Deathday Party, Nearly Headless Nick "shook his letter open and read furiously" when he was rejected from the Headless Hunt. As well, the Deathday Party has "hundreds of translucent people" including an orchestra of about thirty who are playing musical saws.
And, while not a ghost, but a poltergeist, we all know that Peeves handles object frequently (And with unrelenting malice!).
The short answer is that we don't know.
The image below (from Pottermore) suggests that he's not able to turn book pages since the books on his desk are covered in dust and cobwebs. While there are a few brief references to him shuffling his "notes" in PoA and GoF, there's no reason to imagine that these aren't simply part of his ghostly personae (e.g. like Nearly Headless Nick's various ruffs).
That said, since ghosts are perfectly capable of interacting with solid matter, it's possible that he could mark OWLS and NEWTS (as well as parchment essays) without the assistance of a student helper, prefect or another teacher.
As any teacher knows, the actual teaching of lessons is only one part of a Professor's role. In order for him not to notice that he's dead, he'll need to be nearly drowning in paperwork at all times.