Strengthening Oversight for Veterans Act of 2021 This bill gives the Department of Veterans Affairs Office of Inspector General (VA OIG) the authority to subpoena the attendance and testimony of witnesses as necessary to carry out the duties of the office. The bill prohibits the VA OIG from subpoenaing the attendance and testimony of current federal employees or witnesses as part of any criminal proceeding. Under the bill, the VA OIG must notify the Department of Justice (DOJ) and the intended witness of the intent to issue a subpoena. If DOJ objects to the subpoena because it will interfere with an ongoing investigation, the VA OIG may not issue the subpoena.