Long non-coding RNAs (lncRNAs) and microRNAs (miRNAs) are crucial non-coding RNAs involved in various diseases. Understanding these interactions is vital for advancing diagnostic, preventive, and therapeutic strategies. Existing computational methods often address lncRNA-miRNA-disease associations as isolated tasks, resulting in sparse connections and limited generalizability. Additionally, these ncRNA-disease relationships involve higher-order topological information that is frequently overlooked. To address these challenges, we propose the MTL-NRDA model, which employs a multi-task learning framework to simultaneously predict lncRNA-disease associations, miRNA-disease associations, and lncRNA-miRNA interactions. The model integrates multi-source information through a heterogeneous network encompassing lncRNAs, miRNAs, and disease association networks as well as various similarity networks. Node embeddings are optimized by combining local and global contexts, and local features are aggregated using higher-order graph convolutional networks (HOGCN) to capture ncRNA-disease associations, while global features are extracted via a transformer encoder, effectively handling long-range dependencies. MTL-NRDA uses independent bilinear output layers for each task and dynamically adjusts the loss weights to calculate task-specific association probabilities. Experiments on two independent datasets show that MTL-NRDA outperforms existing models. Ablation studies confirmed the effectiveness of the model components and multi-task strategy, whereas hyperparameter tuning further improved the performance. Case studies on breast and liver cancers demonstrated the practical applicability of the model.