The classical stability analysis is used to examine the combined effect of viscoelasticity, thermal and mechanical anisotropic effects on the onset of porous medium ferroconvection. The fluid and solid matrix are assumed to be in local thermal equilibrium. Considering the boundary conditions appropriate for an analytical approach, the critical values pertaining to both stationary and oscillatory instabilities are obtained by means of the normal mode analysis. It is delineated that oscillatory instability is preferred to stationary instability depending on the range of various parameters. It is also shown that oscillatory porous medium ferroconvection is advanced through the magnetic forces, nonlinearity in magnetization, stress relaxation due to viscoelasticity and the mechanical anisotropy. On the other hand, it is observed that the presence of the stress retardation and the thermal anisotropy delay the onset of oscillatory porous medium ferroconvection. The effect of various parameters on the size of the convection cell is also discussed. The results of the problem may have possible implications for engineering and technological applications wherein magnetic fluids are encompassed along with the viscoelastic and anisotropic properties.