Sodium-based batteries are gaining momentum due to the abundance and lower cost of sodium compared to lithium. Solid-state sodium batteries can also provide further safety advantages. However, sodium-based solid-state electrolytes (SSEs) that meet all the rigorous requirements, such as high ionic conductivity, oxidative stability with the cathode, and ease of processability, are lacking. We present here a new class of sodium-based oxyhalide electrolytes NaNbCl6-2xOx with a facile mechanochemical synthesis. The oxyhalide NaNbCl4O exhibits close to two orders of magnitude higher ambient-temperature sodium-ion conductivity (1.03 x 10-4 S cm-1) compared to the halide counterpart NaNbCl6 (3 x 10-6 S cm-1). Structural motifs unique to the oxygen content in NaNbCl6-2xOx are identified with 23Na and 93Nb magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopy and x-ray diffraction (XRD). Solid-state sodium batteries assembled with NaNbCl4O electrolyte and the cobalt- and nickel-free layered Na0.70Fe0.3Mn0.65Al0.05O2 cathode exhibit a maximum discharge capacity of 155 mA h g-1 with good cycle life at ambient temperature.