Accurately recognizing human context from smartphone sensor data remains a significant challenge, especially in sedentary settings where activities such as studying, attending lectures, relaxing, and eating exhibit highly similar inertial patterns. Furthermore, social context plays a critical role in understanding user behavior, yet is often overlooked in mobile sensing research. To address these gaps, we introduce LogMe, a mobile sensing application that passively collects smartphone sensor data (accelerometer, gyroscope, magnetometer, and rotation vector) and prompts users for hourly self-reports capturing both sedentary activity and social context. Using this dual-label dataset, we propose DySTAN (Dynamic Cross-Stitch with Task Attention Network), a multi-task learning framework that jointly classifies both context dimensions from shared sensor inputs. It integrates task-specific layers with cross-task attention to model subtle distinctions effectively. DySTAN improves sedentary activity macro F1 scores by 21.8% over a single-task CNN-BiLSTM-GRU (CBG) model and by 8.2% over the strongest multi-task baseline, Sluice Network (SN). These results demonstrate the importance of modeling multiple, co-occurring context dimensions to improve the accuracy and robustness of mobile context recognition.