Accurately predicting conversion rate (CVR) is paramount in online advertising. However, traditional models may face problems such as delayed feedback, where there is a delay of an indeterminate amount of time between click and conversion. Calibration is an effective way to optimize conversion rate estimates in online advertising. Unlike conversion delays, post-click user behaviors occur rapidly and are informative to conversion rate prediction. Our proposed solution, the Multi-Task Mixture-of-Experts Calibration (MTMEC) framework, integrates multi-task learning and mixture-of-experts models. It modifies CVR prediction using post-click user behavior data, utilizing streaming learning for real-time data access. Each task is weighted by a gating network, enabling adaptive loss functions through multi-task learning. Parametric scaling further minimizes calibration errors, enhancing prediction accuracy without excessive parameters. Experiments on real-world datasets validate the effectiveness of MTMEC. It improves model prediction and reduces calibration errors. This framework offers a robust solution for online advertising, bridging the gap between calibration accuracy and system responsiveness.