<p>Detecting anomalies on social media has become increasingly important because of the massive scale, constant growth, and ever-changing nature of user-generated content. This paper takes a closer look at how lightweight large language models (LLMs) can be used to build efficient anomaly detection systems that handle high data volumes, evolving malicious strategies, and resource limitations. Traditional methods often fall short when faced with the complexity and scale of social media, whereas lightweight LLMs strike a practical balance between speed, accuracy, and efficiency. They are especially promising for real-time monitoring on devices with limited computing power. The review is based on a systematic search of major academic databases, using keywords such as anomaly detection, fake news detection, lightweight LLMs, and resource-efficient NLP models. Only studies that focused directly on social media anomaly detection and lightweight architectures were included, while purely theoretical or unrelated works were excluded. Key challenges identified include scalability, managing false positives and false negatives, and concerns around privacy, transparency, and interpretability of the models. Looking ahead, the study points to several promising directions: applying federated learning for privacy-preserving solutions, leveraging explainable AI to improve transparency, and adopting multimodal approaches that integrate text, images, and network data for stronger detection performance. Overall, this review highlights how lightweight LLMs can support the development of efficient, scalable, and adaptable solutions for anomaly detection in social media.</p>