This paper reviews advanced optimization techniques to address the privacy-utility tradeoff in federated learning with differential privacy (FL-DP), focusing on applications in the Internet of Medical Things (IoMT). IoMT systems face significant challenges, including heterogeneous, non-IID data distributions, resource-constrained devices, and stringent privacy regulations such as HIPAA and GDPR, making it complex to ensure robust privacy while maintaining high model utility. The review explores methods such as adaptive privacy budgeting, which dynamically adjusts privacy parameters (∈) based on data sensitivity and device capabilities, and client selection strategies that enhance global model accuracy by prioritizing high-quality data contributions while effectively managing privacy budgets. Techniques like gradient clipping and noise scaling are examined for their ability to mitigate the negative impact of differential privacy (DP) noise, ensuring stability in real-time applications like remote patient monitoring and anomaly detection. This study analyzes existing techniques and identifies gaps in advancing scalable and efficient FL-DP frameworks in IoMT. Future directions include AI-driven adaptive privacy mechanisms and energy-efficient optimization algorithms to enhance the scalability, performance, and sustainability of FL-DP in IoMT environments. These advancements aim to develop secure, high-performance IoMT systems that comply with privacy standards while addressing real-world healthcare challenges.