Recent advancements in Natural Language Processing and Deep Learning have enabled the development of Large Language Models (LLMs), which have significantly advanced the state-of-the-art across a wide range of tasks, including Question Answering (QA). Despite these advancements, research on LLMs has primarily targeted high-resourced languages (e.g., English), and only recently has attention shifted toward multilingual models. However, these models demonstrate a training data bias towards a small number of popular languages or rely on transfer learning from high- to under-resourced languages; this may lead to a misrepresentation of social, cultural, and historical aspects. To address this challenge, monolingual LLMs have been developed for under-resourced languages; however, their effectiveness remains less studied when compared to multilingual counterparts on language-specific tasks. In this study, we address this research gap in Greek QA by contributing: (i) DemosQA, a novel dataset, which is constructed using social media user questions and community-reviewed answers to better capture the Greek social and cultural zeitgeist; (ii) a memory-efficient LLM evaluation framework adaptable to diverse QA datasets and languages; and (iii) an extensive evaluation of 11 monolingual and multilingual LLMs on 6 human-curated Greek QA datasets using 3 different prompting strategies. We release our code and data to facilitate reproducibility.