ODAR stands for the Office of Disability Adjudication and Review. It is a branch of the Social Security Administration. Once you have been denied for disability benefits and your appeal is also denied, you file a request for a hearing. At this point your case is forwarded to ODAR.
You will receive various letter from ODAR over the course of your hearing including confirmation that your case was received and notification of when your hearing date is.
The Office of Disability Adjudication and Review holds the hearings and issues the decisions regarding whether or not you will receive disability benefits. There are over 160 hearing offices with more than 1,600 Administrative Law Judges across the nation. It is these ALJs that hear your final appeal and determine whether you will receive benefits of not.