Super-resolution infrared compressive imaging (SR-IRCI) is an emerging computational imaging technology that effectively enhances the spatial resolution and detailed features of infrared images captured by low-resolution detectors. However, non-ideal factors such as diffraction, aberrations, pixel mismatch and alignment errors in the SR-IRCI system inevitably degrade the reconstruction quality of high-resolution images. Furthermore, existing system calibration methods based on complex manual operations are inefficient and repetitive. To overcome these shortcomings, this paper develops a high-order physical model for SR-IRCI to comprehensively characterize and incorporate the interference of non-ideal factors in the image reconstruction process. In addition, a learning-based calibration approach is developed that can achieve persistently valid system parameters through single-calibration operation. Thus, the cumbersome re-calibration operations can be avoided when changing different coded apertures. An SR-IRCI prototype is built and the superiority of the proposed methods is demonstrated by both simulations and experiments.