Bringing artificial intelligence on board Earth observation satellites unlocks unprecedented possibilities to extract actionable items from various image modalities at the global scale in real time. This is of paramount importance nowadays, as downlinking large amounts of imagery is not only prohibitively expensive but also time-consuming. However, building deep learning solutions that could be deployed on board an edge device is challenging due to the limited manually-annotated satellite datasets and hardware constraints of an edge device. This paper addresses these challenges through harnessing a blend of data-centric and model-centric approaches to build a well-generalizing yet efficient and resource-frugal deep learning model for multi-class satellite image classification in the few-shot learning settings. This integrated strategy is formulated to enhance classification performance while accommodating the unique demands of an image analysis chain on board OPS-SAT, a nanosatellite operated by the European Space Agency. The experiments performed over a real-world dataset of OPS-SAT images delves into the interactions between data- and model-centric techniques, underscores the significance of synthesizing artificial training data and emphasizes the value of ensemble learning. However, they also caution against negative transfer in domain adaptation. This study sheds light on effective model training strategies and highlights the multifaceted challenges inherent in deep learning for practical Earth observation, contributing insights to the field of satellite image classification within the constraints of nanosatellite operations. To ensure reproducibility of our study, the implementation is available at https://github.com/ShendoxParadox/Few-shot-satellite-image-classification-OPS-SAT.