Oil Spill Victims Redress Act - Amends the Oil Pollution Act of 1990 to: (1) require all claims against each responsible party for removal costs or damages under such Act to be presented first to the responsible party or guarantor of the source of the discharge or threat; (2) authorize a state court to award damages or other relief to any person for claims under state law against any responsible party or other person; (3) provide that a civil action brought in state court with respect to a discharge of oil into or on the navigable waters, adjoining shorelines, or the state's exclusive economic zone is not within the original jurisdiction of the U.S. district courts, and is therefore not removable, unless a federal claim is pleaded in addition to claims arising under state law or the action is otherwise removable based on diversity of citizenship; and (4) provide that nothing in such Act shall affect or preempt the authority of any state from imposing on any responsible party or other person any additional liability or requirement with respect to the discharge of oil occurring within the state, pollution by oil having effects within the state, or any removal activities in connection with such discharge.