Strategic and Humane Southern Border Migrant Response Act This bill imposes requirements related to the handling of migrants from Northern Triangle countries (El Salvador, Guatemala, and Honduras) and terminates certain policies requiring asylum seekers to wait in Mexico before applying and while cases are pending. The President shall report on a plan for processing asylum seekers apprehended at the U.S.-Mexico border. The Department of Homeland Security (DHS) shall establish a task force to implement the plan. Customs and Border Protection (CBP) shall maintain family unity to the greatest extent possible, unless there is a legal requirement or safety concern requiring otherwise. DHS shall (1) make every effort to ensure that apprehended individuals have access to bathrooms and showers, water, appropriate nutrition, hygiene, and sanitation (currently, the statute only requires access to food and water); (2) establish uniform medical screening procedures for detained individuals and programs that provide alternatives to detention; (3) increase its capacity to care for families and unaccompanied children by contracting with qualified entities and hiring additional CBP officers; and (4) restore a program that allowed certain minors in Northern Triangle countries to apply for refugee status without traveling to the United States. The Government Accountability Office and DHS Inspector General shall audit and conduct uninspected inspections of detention facilities. Any Member of Congress may inspect such facilities without prior notification The Department of State shall work with the United Nations to increase the capacity of Northern Triangle countries and Mexico to handle and care for those seeking refugee resettlement.