This paper theoretically proposes a multichannel nonlocal metasurface computer characterized by generalized sheet transition conditions (GSTCs) and surface susceptibility tensors. The study explores polarization- and angle-multiplexed metasurfaces enabling multiple and independent parallel analog spatial computations when illuminated by differently polarized incident beams from different directions. The proposed synthesis overcomes substantial restrictions imposed by the previous designs such as large architectures arising from the need for additional sub-blocks; slow responses; working for a certain incident angle or polarization; executing only a single mathematical operation; and, most importantly, supporting only the even-symmetric operations for normal incidences. The versatility of our design is demonstrated in a way that an ultracompact, integrable, and homogeneous metasurface-assisted platform can execute a variety of optical-signal-processing operations such as spatial differentiation and integration. It is demonstrated that a metasurface featuring nonreciprocal properties can be thought of as a new paradigm to break the even symmetry of reflection and perform both even- and odd-symmetric mathematical operations for input fields coming from a normal direction. Numerical simulations also illustrate different aspects of a multichannel edge detection scheme through projecting multiple images on the metasurface from different directions. Such appealing findings not only circumvent the major potential drawbacks of previous designs but may also offer an efficient, easy-to-fabricate, and flexible approach in wave-based signal processing, edge detection, image contrast enhancement, hidden object detection, and equation solving without a Fourier lens.