The present study is devoted to the Mn2.4Fe0.8Al0.8 and Mn2FeAl alloys prepared by induction melting and studied in their original and subsequently annealed states. The annealing was carried out at 773 K/100 h and 1073 K/100 h in the argon atmosphere. The microstructure, phase composition, magnetic properties, and atom arrangement are followed with regard to Mn content and annealing conditions.The scanning electron microscopy completed by the energy dispersive X-ray spectroscopy and neutron activation analysis has detected single-phase alloys with compositions close to the nominal ones. Their structure, analyzed by X-ray diffraction, was found to be primitive cubic β-Mn with the lattice parameters of 0.6359(2) nm for Mn2.4Fe0.8Al0.8 and 0.6339(1) nm for Mn2FeAl. The coherent potential approximation calculations and positron annihilation spectroscopy have allowed obtaining an overview to the arrangement of Mn, Fe, and Al atoms in the β-Mn structure and formation of the open volume defects. It is shown that Mn atoms occupy predominantly 8c Wyckoff sites and remaining Mn, Fe and Al atoms occupy 12d sites in equal 1/3 proportion. The open volume defects, vacancies and vacancy clusters, occur in both alloys and both annealed states in a very low concentration. From the magnetic viewpoint, both alloys in the as-prepared state and after annealing at 773 K/100 h are paramagnetic at room temperature with transition to antiferromagnetic state at about 30-40 K. The ac susceptibility measurements have indicated spin glass nature of the Mn2FeAl alloys. The annealing at a higher temperature, 1073 K/100 h, has affected mainly Mn2.4Fe0.8Al0.8 alloy manifesting a weak ferro-/ferrimagnetic contribution at room temperature contributing to a strong magnetic ordering below 42 K.