Emergency Housing Voucher Act of 2020 This bill authorizes the Department of Housing and Urban Development to provide emergency rental assistance vouchers to public housing agencies (PHAs) to administer to eligible low-income families. In administering such vouchers, PHAs must give preference to families that are (1) homeless; (2) at risk of homelessness; or (3) fleeing, or attempting to flee, domestic violence, dating violence, sexual assault, or stalking.