A new approach utilizing effects of dispersion in the high-order-mode fibers (HOMFs) to effectively discriminate changes in environmental temperature and axial strain is proposed and experimentally demonstrated. Experimental characterization of a HOMF-based fiber modal interferometer with a sandwich fiber structure exhibits excellent agreements with numerical simulation results. A Fourier transform method of interferometry in the spatial frequency domain is adopted to distinguish mode coupling between different core-guided modes. Distinct phase sensitivities of multiple dispersion peaks are extracted by employing a novel phase demodulation scheme to realize dual-parameter sensing.