Military Housing Oversight and Service Member Protection Act This bill modifies various provisions related to the contracting and provision of privatized military housing. Among other requirements, DOD must establish formal written requirements and guidance for entering into and renewing contracts related to the acquisition and improvement of military housing, employ a sufficient number of independent housing inspectors with appropriate certifications to conduct inspections without notice to landlords, provide oversight to ensure that maintenance for such housing units is completed in accordance with applicable health and building codes, publish the financial details of each contract for the management of housing units, and ensure all military medical treatment facilities screen members of the armed forces or their family members who have resided in unsafe housing units. The bill also extends legal protections afforded to tenants located in a jurisdiction surrounding a military instillation to tenants residing in housing located on a military installation, establishes a presumption of service-connection for certain conditions that are determined to be associated with residing in privatized military housing, provides Department of Veterans Affairs health care for conditions associated with residing in privatized military housing to a family member of a veteran (including a child in utero) during a specified time period, and prohibits specified individuals from owning interest in an entity that owns or manages privatized military housing. DOD is authorized to modify any contract entered into regarding privatized military housing to conform to changes made by this bill.