Ordering of interpolated Ba2+ chains and alternate Ta-O rows (TaO)(3+) in the pentagonal tunnels of tetragonal tungsten bronzes (TTB) is controlled by the nonstoichiometry in the highly nonstoichiometric Ba0.5-xTaO3-x system. In Ba0.22TaO2.72, the filling of Ba2+ and (TaO)(3+) groups is partially ordered along the ab-plane of the simple TTB structure, resulting in a root 2-type TTB superstructure (Pbmm), while in Ba0.175TaO2.675, the pentagonal tunnel filling is completely ordered along the b-axis of the simple TTB structure, leading to a triple TTB superstructure (P2(1)2(1)2). Both superstructures show completely empty square tunnels favoring Ba2+ conduction and feature unusual accommodation of Ta5+ cations in the small triangular tunnels. In contrast with stoichiometric Ba6GaTa9O30, which shows linear thermal expansion of the cell parameters and monotonic decrease of permittivity with temperature within 100-800 K, these TTB superstructures and slightly nonstoichiometric simple TTB Ba0.4TaO2.9 display abnormally broad and frequency-dependent extrinsic dielectric relaxations in 10(3)-10(5) Hz above room temperature, a linear deviation of the c-axis thermal expansion around 600 K, and high dielectric permittivity similar to 60-95 at 1 MHz at room temperature.