The microwave sensitivity of a spin diode consisting of a tunnel junction with two magnetic electrodes is investigated. The specific feature of the magnetic tunnel structure under consideration is a skew of the electrode magnetizations in the plane of the layers, arising due to exchange interaction with the adjacent antiferromagnetic layers with different superparamagnetic blocking temperatures. Within the framework of the macrospin model the stability analysis of the stationary magnetization states is carried out as a function of the electric current and the skew angle between the magnetizations of the magnetic layers on the angle-current plane, taking into account the effect of spin torque transfer. For the obtained stationary states, variations of the resonant response to an ac current of microwave range and volt-watt sensitivity of the spin diode far away from and near the critical bias-current lines of the transition to self-oscillations are determined. It is shown that with increasing the bias current upon the approach to the critical point, hysteresis of the frequency branches of resonant response appears, induced by the nonlinear microwave modulation of torque. This effect is different from the foldover-effect under the condition of initial Lorentzian character of the ferromagnetic resonance with a constant linewidth. Furthermore, micromagnetic simulation of the diode sensitivity for similar magnetic parameters is carried out.