In this paper, a new sensor system for simultaneous and independent multipoint strain and temperature measurements is presented. The interrogation of the sensing heads has been carried out by monitoring their FFT phase variations. In particular, two of each microstructured optical fiber (MOF) cavity interference frequencies were used for the measures. This method is independent of the signal amplitude and also avoids the necessity of tracking the wavelength evolution in the spectrum, which can be a handicap when there are multiple interference frequency components with different sensitivities. The sensing heads present birefringent and multimodal properties and therefore both characteristics lead to their own interference with different properties and sensitivities. The multiplexing capability of the sensing heads and the interrogator method has also been tested and validated. Sensors were operated within a range of temperature 30°C-80°C and a deformation of ~450 was applied. Crosstalk between measurements can be corrected through simple math operations leading to independent and crosstalk-free multipoint and multiparameter sensors.