These indefinite pronouns for the most part follow the same pattern of notional agreement as the other indefinite pronouns: they regularly take a singular verb but may be referred to by either a singular or plural pronoun. The handbooks that take a traditional position—mostly older ones—insist on the singular pronoun; newer ones recognize plural reference, although some of them avoid actual approval by limiting they, their, and them to informal use. Formal agreement looks like this:
Nobody attains reality for my mother until he eats —Flannery O'Connor, letter, 28 June 1956
You can see right away one of the problems that formal singular agreement brings up—the question of sexism, conscious or otherwise. So there is an added advantage to favoring the plural pronoun: you avoid having to decide whether to use he or she, his or her, or him or her. Sometimes the notion of the many is so strong that the context simply calls for a plural:
No one believes (they are right) —Adolf A. Berle, The Reporter, 8 Sept. 1955
... but nobody really wanted to hear him speak. They wanted to see him grin —Harry S. Truman, quoted in Merle Miller, Plain Speaking, 1973
And the plural pronoun is often used even when the singular would present no problem:
Nobody here seems to look into an Author, ancient or modern, if they can avoid it —Lord Byron, letter, 12 Nov. 1805
Byron was writing from Cambridge, and his reference could only have been to males. But he used the plural they anyway.
The use of the plural pronoun in reference to nobody and no one is not only very common, it is well established—the OED dates it back as far as 1548. It is as old-fashioned as Jane Austen and as modern as Doris Lessing:
Nobody was in their right place —Jane Austen, Mansfield Park, 1814
... nobody minds having what is too good for them —Jane Austen, Mansfield Park, 1814
"But nobody uses it, do they?" —Doris Lessing, The Good Terrorist, 1985
Our advice to you is to not be afraid of using they, their, or them to refer to nobody or no one when the idea is clearly plural (as it is in the Berle and Truman examples above) or when you simply want to avoid a choice between masculine and feminine singular pronouns. When the sense is not necessarily plural, you can use singular pronouns in accordance with formal agreement. But meaning should come first.