Emotion Recognition in Conversations (ERC) facilitates a deeper understanding of the emotions conveyed by speakers in each utterance within a conversation. Recently, Graph Neural Networks (GNNs) have demonstrated their strengths in capturing data relationships, particularly in contextual information modeling and multimodal fusion. However, existing methods often struggle to fully capture the complex interactions between multiple modalities and conversational context, limiting their expressiveness. To overcome these limitations, we propose ConxGNN, a novel GNN-based framework designed to capture contextual information in conversations. ConxGNN features two key parallel modules: a multi-scale heterogeneous graph that captures the diverse effects of utterances on emotional changes, and a hypergraph that models the multivariate relationships among modalities and utterances. The outputs from these modules are integrated into a fusion layer, where a cross-modal attention mechanism is applied to produce a contextually enriched representation. Additionally, ConxGNN tackles the challenge of recognizing minority or semantically similar emotion classes by incorporating a re-weighting scheme into the loss functions. Experimental results on the IEMOCAP and MELD benchmark datasets demonstrate the effectiveness of our method, achieving state-of-the-art performance compared to previous baselines.