In this thesis, we address the data scarcity and limitations of linguistic theory by proposing language-agnostic multi-task training methods. First, we introduce a meta-learning-based approach, meta-transfer learning, in which information is judiciously extracted from high-resource monolingual speech data to the code-switching domain. The meta-transfer learning quickly adapts the model to the code-switching task from a number of monolingual tasks by learning to learn in a multi-task learning fashion. Second, we propose a novel multilingual meta-embeddings approach to effectively represent code-switching data by acquiring useful knowledge learned in other languages, learning the commonalities of closely related languages and leveraging lexical composition. The method is far more efficient compared to contextualized pre-trained multilingual models. Third, we introduce multi-task learning to integrate syntactic information as a transfer learning strategy to a language model and learn where to code-switch. To further alleviate the aforementioned issues, we propose a data augmentation method using Pointer-Gen, a neural network using a copy mechanism to teach the model the code-switch points from monolingual parallel sentences. We disentangle the need for linguistic theory, and the model captures code-switching points by attending to input words and aligning the parallel words, without requiring any word alignments or constituency parsers. More importantly, the model can be effectively used for languages that are syntactically different, and it outperforms the linguistic theory-based models.