The main challenge of sodium-ion batteries is cycling stability, which is usually compromised due to strain induced by sodium insertion. Reliable high-voltage cathode materials are needed to compensate the generally lower operating voltages of Na-ion batteries compared to Li-ion ones. Herein, density functional theory (DFT) computations were used to evaluate the thermodynamic, structural, and kinetic properties of the high voltage λ-Mn2O4 and λ-Mn1.5Ni0.5O4 spinel structures as cathode materials for sodium-ion batteries. Determination of the enthalpies of formation reveal the reaction mechanisms (phase separation vs solid solution) during sodiation, while structural analysis underlines the importance of minimizing strain to retain the metastable sodiated phases. For the λ-Mn1.5Ni0.5O4 spinel, a thorough examination of the Mn/Ni cation distribution (dis/ordered variants) was performed. The exact sodiation mechanism was found to be dependent on the transition metal ordering in a similar fashion to the insertion behavior observed in the Li-ion system. The preferred reaction mechanism for the perfectly ordered spinel is phase separation throughout the sodiation range, while in the disordered spinel, the phase separation terminates in the 0.625 < x < 0.875 concentration range and is followed by a solid solution insertion reaction. Na-ion diffusion in the spinel lattice was studied using DFT as well. Energy barriers of 0.3-0.4 eV were predicted for the pure spinel, comparing extremely well with the ones for the Li-ion and being significantly better than the barriers reported for multivalent ions. Additionally, Na-ion macroscopic diffusion through the 8a-16c-8a 3D network was demonstrated via molecular dynamics (MD) simulations. For the λ-Mn1.5Ni0.5O4, MD simulations at 600 K bring forward a normal to inverse spinel half-transformation, common for spinels at high temperatures, showing the contrast in Na-ion diffusion between the normal and inverse lattice. The observed Ni migration to the tetrahedral sites at room temperature MD simulations explains the kinetic limitations experienced experimentally. Therefore, this work provides a detailed understanding of the (de)sodiation mechanisms of high voltage λ-Mn2O4 and λ-Mn1.5Ni0.5O4 spinel structures, which are of potential interest as cathode materials for sodium-ion batteries.