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Static and dynamic magnetic properties of the five members of A2MnXO4 (A = Li, Na, Ag; X = Si, Ge) family, including four new phases have been comprehensively studied experimentally by magnetization, heat capacity and ESR measurements as well as theoretically by density functional calculations. It was found that the magnetic susceptibility and specific heat data reveal the onset of long-range antiferromagnetic order in all systems of the A2MnXO4 family under study, except for Ag2MnSiO4 which remains in the paramagnetic state down to 2 K. The magnetization isotherms indicate a magnetic field induced spin-reorientation (spin-flop type) transition at T < TN for all antiferromagnetic systems implying two different spin-configurations in the ordered phases. The spin-flop fields of about 2 T imply small magnetic anisotropy gaps of D = 0.23 meV. Summarizing the thermodynamic data in magnetic fields up to 9 T the magnetic phase diagrams of Li2MnxO4 (X = Si, Ge) and Na2MnXO4 (X = Si, Ge) have been constructed for the first time. The dynamic magnetic properties obtained from X-band ESR technique corroborate very well the static magnetic data. In addition, the data show an extended temperature range of short-range magnetic correlations which is characteristic of low-dimensional and frustrated materials. The experimental findings are well supported by means of density functional theoretical analysis, which allow to estimate the main exchange parameters and to propose the possible spin-configuration structures for all systems under study.