Presently, adsorption/absorption is one of the most efficient and cost-effective methods to clean oil spill up. In this work, self-supporting paper-like fibrous membranes were prepared via electrospinning and carbonisation at different temperatures (500, 650 or 800 °C) by using polyacrylonitrile/polymethylmethacrylate blends with a different mass ratio of the two polymers (1:0, 6:1 or 2:1). After morphological and microstructural characterisation, the as-produced membranes were evaluated as sorbents by immersion in vegetable (sunflower seed or olive) and mineral (motor) oil or in 1:4 (v:v) oil/water mixture. Nitrogen-rich membrane carbonised at the lowest temperature behaves differently from the others, whose sorption capacity by immersion in oil, despite the great number of sorbent and oil properties involved, is mainly controlled by the fraction of micropores. The encapsulation of water nanodroplets by the oil occurring during the immersion in oil/water mixture causes the oil-from-water separation ability to show an opposite behaviour compared to the sorption capacity. Overall, among the investigated membranes, the support produced with 2:1 mass ratio of the polymers and carbonisation at 650 °C exhibits the best performance both in terms of sorption capacity (73.5, 54.8 and 12.5 g g−1 for olive, sunflower seed and motor oil, respectively) and oil-from-water separation ability (74, 69 and 16 for olive, sunflower seed and motor oil, respectively).