Background: The rapid growth of IoT and edge devices demands low-latency, scalable computing solutions. Traditional cloud architectures introduce bottlenecks, while serverless computing, particularly Function-as-a-Service (FaaS), offers an event-driven, on-demand execution model. However, existing FaaS platforms rely on centralized orchestration, leading to cold start delays, resource inefficiencies, and limited adaptability in edge environments. This study examines containerized workload management for serverless edge computing, evaluating orchestration, choreography, and offloading techniques to improve function execution efficiency and system scalability. Objective: The aim of this work is to conduct a systematic review the state-of-the-art practices in orchestration and offloading techniques for containerized environments. Method: We conducted a Multivocal Literature Review, selecting 94 works from a pool of 771. Results: The offloading strategies rely on a central orchestrator and on the use of well-established tools such as Kubernetes and Docker. Few studies propose alternatives, highlighting a lack of diversity in offloading tools. These studies underscore a significant lack of diversity in the tools used for offloading in containerized systems. Conclusion: We have identified key strengths and limitations of the existing approaches. These limitations are primarily related to response time, performance, and resource utilization.