With maturation of 5G technology in recent years, multimedia services such as live video streaming and online games on the Internet have flourished. These multimedia services frequently require low latency, which pose a significant challenge to compute the high latency requirements multimedia tasks. Mobile edge computing (MEC), is considered a key technology solution to address the above challenges. It offloads computation-intensive tasks to edge servers by sinking mobile nodes, which reduces task execution latency and relieves computing pressure on multimedia devices. In order to use MEC paradigm reasonably and efficiently, resource allocation has become a new challenge. In this paper, we focus on the multimedia tasks which need to be uploaded and processed in the network. We set the optimization problem with the goal of minimizing the latency and energy consumption required to perform tasks in multimedia devices. To solve the complex and non-convex problem, we formulate the optimization problem as a distributed deep reinforcement learning (DRL) problem and propose a federated Dueling deep Q-network (DDQN) based multimedia task offloading and resource allocation algorithm (FDRL-DDQN). In the algorithm, DRL is trained on the local device, while federated learning (FL) is responsible for aggregating and updating the parameters from the trained local models. Further, in order to solve the not identically and independently distributed (non-IID) data problem of multimedia devices, we develop a method for selecting participating federated devices. The simulation results show that the FDRL-DDQN algorithm can reduce the total cost by 31.3% compared to the DQN algorithm when the task data is 1000 kbit, and the maximum reduction can be 35.3% compared to the traditional baseline algorithm.