Typically host families don't get paid much, however, when they do the 1099 reporting is inconsistent. Some report it as other income, some as rent, some as nonemployee compensation. This is a transaction that is unique in the sense that there is no formal guidance by the IRS on how to treat this. 

Typically host families do not get paid more than the cost of hosting an exchange student. Thus, the presumption is that this is an activity not engaged for profit under §183- which deductions follow the normal ordering rules under this code section. This means the income is reported on Line 21 of Form 1040. Deductions would fall under 2% itemized deductions on Schedule A. 

If, however, based on facts and circumstances, such as fair-market value rent, you may be able to establish this as rental of personal home under §280A, or if they are more active in this such as cleaning the room and cooking for such student, as a schedule C if they perform many services related to room and board. The simple answer is "yes" deductions can be taken, but to what extent and where depends on how this activity is conducted.