This is not an exhaustive list, but here are a few organizations offering services to immigrants and refugees. They always need more volunteers.
Americana World Community Center
366-7813
americanacc.org
Kentucky Refugee Ministries
479-9180
kyrm.org
Catholic Charities of Louisville
637-9786, ext. 204
cclou.org
And…. the Louisville Free Public Library hosts an English conversation club several times a week, in different locations. It always needs more English speakers to give new Louisvillians a chance to practice.