None of the three sentences you wrote is ungrammatical. However, the sentences differ in meaning.
writing on the paper
This implies that the students were all drawing their own illustrations on the same sheet of paper. Perhaps it was a large sheet draped over all their desks.
writings on the papers
This implies that there were several sheets of paper. Perhaps each student has their own.
writing on the papers
This likewise implies that there were several sheets of paper, perhaps with each student having their own.
If you want the sentence to be consistent with each student having their own piece of paper, I would suggest that you use the plural "papers". You may use either "writing" or "writings", depending on your preference.
My reasoning is that "writing" may be interpreted as a mass noun in Sentences 1 and 3, and "writings" may be interpreted as a count noun in Sentence 2. However, "paper" is a count noun (i.e., it refers to a sheet of paper, not the material of paper), and thus should be plural if the students are writing on more than one sheet of paper.