The way cells organize actin filaments at the nanoscale and its relation to biomechanical functions still raises many open questions. Polarized fluorescence microscopies (PFM), which quantify fluorophores orientations based on their coupling to excitation or detection light polarization, provide a quantitative approach to this question. These methods, because they are ensemble imaging techniques, are however vulnerable to important sources of bias such as the possible mixture of different overlapping structures, or the overestimation of orientational disorder when fluorophores are not rigidly attached to the structure of interest. To circumvent such biases, we propose in this work a single molecule based polarized detection together with direct stochastic optical reconstruction microscopy (dSTORM), a method called polarized-dSTORM. We developed a technique based on four polarization projections of STORM images (4Polar-dSTORM) to retrieve, without ambiguity, both averaged orientation and angular fluctuations extent (wobbling) for each single molecule. This approach exhibits strong advantages as compared to previously developed two-polarization projections which required, among others limitations, to suppose identical wobbling for all molecules. We analyzed the effect of tilted illumination and of the detection aperture, to reduce the sensitivity of the method to off-plane 3D-orientation biases that can occur under high numerical aperture conditions. Taking these parameters into account is crucial for a non-biased, quantitative reporter of the orientational behavior of the target protein. We demonstrate the capacity of the method to report the nanoscale organization of actin filaments in cell stress fibers, and study its spatial perturbation when the cell mechanical nature is affected.