We present and discuss an investigation of the sensing features of long period gratings fabricated in a polarization-maintaining Panda optical fiber, by means of the electric arc discharge technique. In particular, the investigation regards the resonant wavelength shift of first three cladding modes as function of three environmental parameters, such as strain, temperature, and surrounding medium refractive index. We also investigate and discuss the variations of the sensing behavior as a function of the polarization input state. The achieved results show that the sensitivity of each resonant wavelength to environmental parameters is modulated by the cladding mode order and by polarization input light, with some appealing characteristics. For instance, the lowest order cladding mode in slow polarization state is practically insensitive to temperature and surrounding refractive index, but sensitive to strain. Temperature and strain sensitivities show opposite signs with the input light polarization. Sensitivity to surrounding refractive index is higher in the case of fast polarization state. These results represent a concrete perspective of the possibility that this device can act as a 3-parameter sensor.