I am currently an off campus student. How can I pay for housing?

You would need to contact your study abroad office in order to see what affiliations you university has with those schools abroad. For example, my school at home is affiliated with Westminster in London so all tuition is transferred over but housing is separate. However, my study abroad program American Institute of Foreign Study (AIFS), similar to you, was cheaper than my tuition usually is at school and this included housing. Since it was with a third party and I stayed with a host family, the fee included tuition, insurance, housing, some meals... etc. All depends on where and who you go through for that specific university.

You should also look at outside scholarships like Gilman, FEA (Fund for Education Abroad), Diversity Abroad, scholarships through your program provider, etc. If you start looking early you should be able to find sufficient funds to cover most of your expenses.