Connected autonomous vehicles (CAVs) must simultaneously perform multiple tasks, such as perception, prediction, planning, and control, to ensure safe and reliable navigation in complex environments. Moreover, through vehicle-to-everything (V2X) communication, cooperative perception and driving among CAVs can be enabled, thereby mitigating the limitations of individual vehicles, while it also introduces stringent latency, reliability, and bandwidth constraints. Traditionally, tasks are addressed using separate models, which leads to high deployment costs, increased computational overhead, and challenges in achieving real-time performance. Multi-task learning (MTL) has recently emerged as a promising solution that enables the joint learning of multiple tasks within a unified model. This offers improved efficiency and resource utilization. To the best of our knowledge, this survey is the first comprehensive review focusing on deep MTL in CAVs. We begin with an overview of CAVs and MTL to provide foundational background. Then, we review MTL approaches across key functional domains in CAVs, including perception, prediction, planning, control, as well as V2X communications and radio resource management (RRM). For the first four domains, we categorize existing works under ego vehicle-only (onboard-only) and V2X-enhanced cooperative (multi-agent) paradigms. We further discuss V2X communications and RRM as communication-centric MTL problems. Finally, we discuss the strengths and limitations of existing methods, identify key research gaps, and provide future research directions aimed at advancing MTL methodologies for CAV systems.