I would say "their" is more encompassing. Putting "their" suggests that everyone in the class, men and women, would receive their homework (since the important word "Every student" suggests more than one student). Also, unless the class is made up of just one sex (all male or all female), using "their" would be safest. It would also be the most logical given that you speak of "people not mentioned before".

The grammatically correct answer is technically "Every student has his or her own task given by the teacher," but as mentioned, when spoken, you'll often hear people use "their": Every student has their task set by their teacher. So the first way is the technically correct way, but the second way is more often used in informal situations.

They and their is now the best answer. From Oxford Dictionaries online: The word they (with its counterparts them, their, and themselves) as a singular pronoun to refer to a person of unspecified gender has been used since at least the 16th century. In the late 20th century, as the traditional use of he to refer to a person of either gender came under scrutiny on the grounds of sexism, this use of they became more common. It is now generally accepted in contexts where it follows an indefinite pronoun such as anyone, no one, someone, or a person, as in anyone can join if they are a resident and each to their own. In other contexts, coming after singular nouns, the use of they is now common, though less widely accepted, especially in formal contexts. Sentences such as ask a friend if they could help are still criticized for being ungrammatical. Nevertheless, in view of the growing acceptance of they and its obvious practical advantages, they is used in this dictionary in many cases where he would have been used formerly. In a more recent development, they is now being used to refer to specific individuals (as in Alex is bringing their laptop). Like the gender-neutral honorific Mx, the singular they is preferred by some individuals who identify as neither male nor female.

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