Despite the significant advancements in Text-to-SQL (Text2SQL) facilitated by large language models (LLMs), the latest state-of-the-art techniques are still trapped in the in-context learning of closed-source LLMs (e.g., GPT-4), which limits their applicability in open scenarios. To address this challenge, we propose a novel RObust mUltitask Tuning and collaboration mEthod (ROUTE) to improve the comprehensive capabilities of open-source LLMs for Text2SQL, thereby providing a more practical solution. Our approach begins with multi-task supervised fine-tuning (SFT) using various synthetic training data related to SQL generation. Unlike existing SFT-based Text2SQL methods, we introduced several additional SFT tasks, including schema linking, noise correction, and continuation writing. Engaging in a variety of SQL generation tasks enhances the model's understanding of SQL syntax and improves its ability to generate high-quality SQL queries. Additionally, inspired by the collaborative modes of LLM agents, we introduce a Multitask Collaboration Prompting (MCP) strategy. This strategy leverages collaboration across several SQL-related tasks to reduce hallucinations during SQL generation, thereby maximizing the potential of enhancing Text2SQL performance through explicit multitask capabilities. Extensive experiments and in-depth analyses have been performed on eight open-source LLMs and five widely-used benchmarks. The results demonstrate that our proposal outperforms the latest Text2SQL methods and yields leading performance.