We design and characterize compact phase-modulated axilens devices that combine efficient point focusing and grating selectivity within four-level phase mask configurations. Specifically, we select and characterize in detail two device configurations designed for long-wavelength infrared (LWIR) operation in the $ 6\,\,\unicode{x00B5}{\rm m}\! -\! 12\,\,\unicode{x00B5}{\rm m} $6µm-12µm wavelength range. These devices are ideally suited for monolithic integration atop the substrate layers of infrared focal plane arrays (IR-FPAs) for use in multiband LWIR photodetection. We systematically study their focusing efficiency, spectral response, and crosstalk ratio, and we demonstrate a single-component microspectrometer. Our design method leverages the Rayleigh-Sommerfeld (RS) diffraction theory that is validated numerically using the finite element method (FEM). The proposed devices are broadband and polarization insensitive and add fundamental spectroscopic capabilities to miniaturized optical components for a number of applications in LWIR detection and spectroscopy.