We have experimentally investigated the multi-parameter sensing characteristics in a novel all-fiber Sagnac loop hybrid interferometer based on a highly birefringent photonic crystal fiber with two asymmetric cores. The sensor device was based on a combination of two types of in-fiber interferences, the intra-core-mode Sagnac interference and the inter-core-mode Mach-Zehnder interference due to the distinct birefringent properties associated with the asymmetric cores. Fast Fourier transform analysis on the transmission spectra of the device exhibited six clear peaks in the spatial frequency domain. By examining the phase shift responses of two distinct Sagnac and one Mach-Zehnder interference peaks, the response matrix that enable simultaneous measurement of torsion, strain, and temperature could be obtained. The proposed all-fiber Sagnac loop hybrid interferometer has the advantages such as simplicity of the device structure, compact device size, and capability for simultaneous sensing of multiple parameters.