If a taxpayer has a disagreement with the IRS and has exhausted all administrative efforts, which courts of original jurisdiction will hear his case? What are the differences between the courts with respect to payment of deficiency before trial, jury trial and types of disputes?

A court of original jurisdiction is a court that has the authority to hear cases. All trial courts must have original jurisdiction. The first trial court that has original jurisdiction over taxpayers' disputes with the IRS is the U.S. Tax Court. The court is located in Washington, D.C.; however, the courts 19 judges will travel to conduct trials in cities across the nation. The U.S. Tax Court hears cases on disputes of insufficient tax payments and tax liability upon transfer of property, among other tax and work-related cases. Parties must file a petition to have their cases heard by the Tax Court (United States Tax Court, "About the Court").If a taxpayer has a complex refund dispute, involving "complex factual and statutory construction issues in tax law," the U.S. Court of Federal Claims will hear the case (United States Court of Federal Claims, "About the Court"). Other cases heard by the court concern government contracts, public contracts, "environmental and natural resources issues," "civilian and military pay claims," Native-American property claim cases against the US, and others ("About the Court"). If a taxpayer wants a tax dispute case tried in a U.S. District Court, the taxpayer must first pay the IRS the disputed amount and request a refund then sue for not receiving the refund. The benefit of having a case heard by the U.S. District Court is that it is the only court in which taxpayers can receive a trial by jury for their tax suits; however, the U.S District Court does not specialize in tax law. If a case is lost in a tax trial court, the losing party always has the option to appeal the decision to the higher appellate courts. There are 12 regional courts of appeal for the 94 federal judicial districts. Should the party want to appeal the case again to an even higher court, the party would next go to the Court of Appeals for the Federal Circuit, which has national jurisdiction. The highest court of appeals is the United States Supreme Court.
http://www.uscfc.uscourts.gov/about-court

https://www.ustaxcourt.gov/about.htm