Offshore Oil and Gas Worker Whistleblower Protection Act of 2019 This bill prohibits an employer from discharging or discriminating against employees working in waters above the Outer Continental Shelf who report or testify about violations of the Outer Continental Shelf Lands Act, including about unsafe conditions or the adequacy of any oil spill response plan required by law. The bill sets forth procedures for the filing, investigation, and adjudication of a whistle-blower complaint. Employers are required to post a notice approved by the Department of Labor explaining employee rights and remedies in a conspicuous workplace location; provide training to employees about their rights within 30 days of employment, and at least once every 12 months thereafter; and provide employees with a card containing a toll-free telephone number for obtaining information or for filing a complaint.