Masks for All Act of 2020 This bill provides funding for the Federal Emergency Management Agency (FEMA) to provide for the manufacture and distribution of high-quality face masks for every individual in the United States during the COVID-19 (i.e., coronavirus disease 2019) emergency. Specifically, the bill directs FEMA to, among other things establish a program to provide three high-quality, reusable face masks to every individual in the United States, including individuals experiencing homelessness and individuals living in group quarters, at no cost, accompanied by specified educational materials; designate face mask pickup sites in each community and provide face masks to each site, allocated according to population, to be distributed to the general public at no cost; consider new designs to create the most comfortable, well-fitting, reusable, and two-way face masks that have adjustable sizing, and if significant improvements in face mask technology are made available, to ensure that such face masks are included in the strategic national stockpile; provide surgical masks and N-95 respirator masks to all individuals working in health care settings in the United States that are experiencing a shortage of such masks, at no cost; and submit to Congress a strategic plan that includes monthly, measurable targets to eliminate shortages and increase domestic production of high-quality masks. The Office of Inspector General of the Department of Homeland Security shall conduct monitoring and oversight of the receipt, disbursement, and use of funds made available under this bill.