Objective. The instability of the EEG acquisition devices may lead to information loss in the channels or frequency bands of the collected EEG. This phenomenon may be ignored in available models, which leads to the overfitting and low generalization of the model. Approach. Multiple self-supervised learning tasks are introduced in the proposed model to enhance the generalization of EEG emotion recognition and reduce the overfitting problem to some extent. Firstly, channel masking and frequency masking are introduced to simulate the information loss in certain channels and frequency bands resulting from the instability of EEG, and two self-supervised learning-based feature reconstruction tasks combining masked graph autoencoders (GAE) are constructed to enhance the generalization of the shared encoder. Secondly, to take full advantage of the complementary information contained in these two self-supervised learning tasks to ensure the reliability of feature reconstruction, a weight sharing (WS) mechanism is introduced between the two graph decoders. Thirdly, an adaptive weight multi-task loss (AWML) strategy based on homoscedastic uncertainty is adopted to combine the supervised learning loss and the two self-supervised learning losses to enhance the performance further. Main results. Experimental results on SEED, SEED-V, and DEAP datasets demonstrate that: (i) Generally, the proposed model achieves higher averaged emotion classification accuracy than various baselines included in both subject-dependent and subject-independent scenarios. (ii) Each key module contributes to the performance enhancement of the proposed model. (iii) It achieves higher training efficiency, and significantly lower model size and computational complexity than the state-of-the-art (SOTA) multi-task-based model. (iv) The performances of the proposed model are less influenced by the key parameters. Significance. The introduction of the self-supervised learning task helps to enhance the generalization of the EEG emotion recognition model and eliminate overfitting to some extent, which can be modified to be applied in other EEG-based classification tasks.