Military Housing Oversight and Service Member Protection Act This bill addresses Department of Defense (DOD) oversight and service member protections in DOD-sponsored private military housing. Among other things, the bill covers contracts, unit inspection, remedying substandard conditions, handling housing-related injuries, and prohibiting improper financial interests by public officials. Specifically, DOD must establish requirements for entering into and renewing contracts with private landlords and must make the financial details of such agreements public. DOD must employ certified independent housing inspectors to ensure that private military housing units are safe, clean, and adequate, and that they meet federal, state, and local laws and standards of habitability. DOD must allow state and local housing inspectors to conduct no-notice inspections, including on military installations. DOD must require each landlord to provide access to the landlord's maintenance work order system. Service members may file a claim with DOD to withhold the basic allowance for housing if a landlord has not met maintenance guidelines or the unit is uninhabitable according to state and local law. Military treatment facilities must screen service members and family members for medical conditions resulting from unsafe private housing, and landlords must pay medical bills associated with housing-related injuries. The Department of Veterans Affairs must provide similar care for veterans and their families. The bill prohibits members of defense-related congressional committees and certain military officers and high-level DOD employees from having a financial interest in private military housing. Violations are subject to civil penalties.