Registration of multi-modal remote sensing images (MRSI) is crucial for unlocking the full potential of heterogeneous remote sensing imagery. However, achieving accurate registration among MRSI is challenging due to the trade-off between geometric invariance and matching accuracy, caused by differences in signal-to-noise ratio and nonlinear radiometric distortion (NRD) arising from varying imaging mechanisms. To tackle the challenge, this paper proposes a lightweight and hybrid feature-guided registration algorithm for MRSI called the hybrid registration algorithm based on multi-dimensional oriented self-similarity features (MOSS). MOSS leverages the advantages of multi-dimensional oriented self-similarity features to progressively enhance registration performance. In the hybrid feature coarse matching stage, oriented self-similarity features are extracted from MRSI, and their directional information is utilized for feature description to estimate the initial affine transformation. The fine matching under multi-dimensional oriented self-similarity features stage takes the outputs of the coarse matching stage to perform a template-like matching process. To evaluate the performance of MOSS, comprehensive experiments are conducted using six different combinations of MRSI, and seven state-of-the-art registration algorithms are selected for comparison. The experimental results demonstrate that MOSS outperforms the compared methods, with the number of correct matches being at least about 1.6 times higher than the comparison methods. Moreover, MOSS exhibits the lowest root mean square error across all experiments, with an average RMSE of 1.86 pixels, achieving an RMSE within 2 pixels. This highlights its effectiveness in achieving precise alignment and robust registration of MRSI.