In the scientific advancement of future cathode materials, alluaudite sodium iron sulfate Na_2+2δFe_2−δ(SO₄)₃ (N_xF_yS) has emerged as one of the most promising candidates for sustainable sodium-ion batteries due to its high Fe^2+/3+ redox potential (3.8 V vs. Na/Na⁺), low cost, and high rate capability. Usually, this material occurs in a non-stoichiometric form with partial Na⁺ substitutions on Fe sites, where δ is close to 0.25 (N_2.5F_1.75S) depending on the synthesis conditions. While many contemporary works have primarily been directed to study this non-stoichiometric compound, our previous theoretical prediction unveiled the possibility to synthesize stoichiometric alluaudite (N₂F₂S), which is expected to deliver higher specific capacity (∼120 mA h g⁻¹) as compared to the non-stoichiometric derivatives. This provokes curiosity toward the non-stoichiometric effect on the electrochemical activities and sodium intercalation mechanism in alluaudite materials. In this work, we therefore perform rigorous first-principles calculations to study the structural evolution, electrochemical behavior, and voltage profile of N_xF_yS with y = 2, 1.75, and 1.5. We reveal the likelihood of two phase transitions after half desodiation process, whereas the probability is reduced with a higher degree of non-stoichiometry, suggesting improvement in the structural reversibility for N_2.5F_1.75S and N₃F_1.5S. The prediction of the voltage profiles shows the benefit of non-stoichiometry in enhancing the specific capacity and identifies the structural rearrangement of Fe₂O₁₀ dimers as the hidden reason behind the irreversible sharp peak experimentally observed in differential galvanostatic profiles.