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In single-molecule super-resolution microscopy, engineered point-spread functions (PSFs) are designed to efficiently encode new molecular properties, such as 3D orientation, into complex spatial features captured by a camera. To fully benefit from their optimality, algorithms must estimate multi-dimensional parameters such as molecular position and orientation in the presence of PSF overlap and model-experiment mismatches. Here, we present a novel joint sparse deconvolution algorithm based on the decomposition of fluorescence images into six basis images that characterize molecular orientation. The proposed algorithm exploits a group-sparsity structure across these basis images and applies a pooling strategy on corresponding spatial features for robust simultaneous estimates of the number, brightness, 2D position, and 3D orientation of fluorescent molecules. We demonstrate this method by imaging DNA transiently labeled with the intercalating dye YOYO-1. Imaging the position and orientation of each molecule reveals orientational order and disorder within DNA with nanoscale spatial precision.