Marine oil spills can cause serious damage to marine ecosystems and biological species, and the pollution is difficult to repair in the short term. Accurate oil type identification and oil thickness quantification are of great significance for marine oil spill emergency response and damage assessment. In recent years, hyperspectral remote sensing technology has become an effective means to monitor marine oil spills. The spectral and spatial features of oil spill images at different levels are different. To accurately identify oil spill types and quantify oil film thickness, and perform better extraction of spectral and spatial features, a multilevel spatial and spectral feature extraction network is proposed in this study. First, the graph convolutional neural network and graph attentional neural network models were used to extract spectral and spatial features in non-Euclidean space, respectively, and then the designed modules based on 2D expansion convolution, depth convolution, and point convolution were applied to extract feature information in Euclidean space; after that, a multilevel feature fusion method was developed to fuse the obtained spatial and spectral features in Euclidean space in a complementary way to obtain multilevel features. Finally, the multilevel features were fused at the feature level to obtain the oil spill information. The experimental results show that compared with CGCNN, SSRN, and A2S2KResNet algorithms, the accuracy of oil type identification and oil film thickness classification of the proposed method in this paper is improved by 12.82%, 0.06%, and 0.08% and 2.23%, 0.69%, and 0.47%, respectively, which proves that the method in this paper can effectively extract oil spill information and identify different oil spill types and different oil film thicknesses.