Domain-generalized few-shot text classification (DG-FSTC) is a new setting for few-shot text classification (FSTC). In DG-FSTC, the model is meta-trained on a multi-domain dataset, and meta-tested on unseen datasets with different domains. However, previous methods mostly construct semantic representations by learning from words directly, which is limited in domain adaptability. In this study, we enhance the domain adaptability of the model by utilizing the distributional signatures of texts that indicate domain-related features in specific domains. We propose a Multi-level Distributional Signatures based model, namely MultiDS. Firstly, inspired by pretrained language models, we compute distributional signatures from an extra large news corpus, and we denote these as domain-agnostic features. Then we calculate the distributional signatures from texts in the same domain and texts from the same class, respectively. These two kinds of information are regarded as domain-specific and class-specific features, respectively. After that, we fuse and translate these three distributional signatures into word-level attention values, which enables the model to capture informative features as domain changes. In addition, we utilize domain-specific distributional signatures for the calibration of feature representations in specific domains. The calibration vectors produced by the domain-specific distributional signatures and word embeddings help the model adapt to various domains. Extensive experiments are performed on four benchmarks. The results demonstrate that our proposed method beats the state-of-the-art method with an average improvement of 1.41% on four datasets. Compared with five competitive baselines, our method achieves the best average performance. The ablation studies prove the effectiveness of each proposed module.