The optimal solution to an optimization problem depends on the problem's objective function, constraints, and size. While deep neural networks (DNNs) have proven effective in solving optimization problems, changes in the problem's size, objectives, or constraints often require adjustments to the DNN architecture to maintain effectiveness, or even retraining a new DNN from scratch. Given the dynamic nature of wireless networks, which involve multiple and diverse objectives that can have conflicting requirements and constraints, we propose a multi-task learning (MTL) framework to enable a single DNN to jointly solve a range of diverse optimization problems. In this framework, optimization problems with varying dimensionality values, objectives, and constraints are treated as distinct tasks. To jointly address these tasks, we propose a conditional computation-based MTL approach with routing. The multi-task DNN consists of two components, the base DNN (bDNN), which is the single DNN used to extract the solutions for all considered optimization problems, and the routing DNN (rDNN), which manages which nodes and layers of the bDNN to be used during the forward propagation of each task. The output of the rDNN is a binary vector which is multiplied with all bDNN's weights during the forward propagation, creating a unique computational path through the bDNN for each task. This setup allows the tasks to either share parameters or use independent ones, with the decision controlled by the rDNN. The proposed framework supports both supervised and unsupervised learning scenarios. Numerical results demonstrate the efficiency of the proposed MTL approach in solving diverse optimization problems. In contrast, benchmark DNNs lacking the rDNN mechanism were unable to achieve similar levels of performance, highlighting the effectiveness of the proposed architecture.