Department of Defense Overdose Data Act of 2023 This bill requires the Department of Defense (DOD) to report annually on the number of overdoses among servicemembers. DOD must also contract with a federally funded research and development center to prepare a report that includes, among other elements, an assessment of current barriers to determining overdose data and recommendations for increasing access to treatment and preventing overdoses. DOD must also establish standards for the distribution of, and training for the use of, naloxone (or other similar medication), opioid disposal materials, fentanyl test strips, and other materials to prevent or reverse overdoses, substance use disorder, or impacts related to substance misuse.