Poppy is a significant pharmaceutical crop, but the seeds and the cold-pressed oil have a big potential as healthy foods. Breeding has mainly focused on agronomical characteristics and alkaloid content. Here, we compared the sensory values, fatty acid and headspace volatile composition of poppy oils and flours produced from different varieties. Two industrial and four culinary varieties were cultivated in our field in 2021–2022. The sensory test differentiated well among varieties. Typical poppy odour and flavour were stronger both in the oils and the flours of the blue-seed varieties compared to the white-seed ones. For most varieties, the harvest year caused no relevant differences. Linoleic, oleic, and palmitic acids were the main components both in oils and flours. Larger differences were detected in the volatiles (e.g., 2 and 3 methyl-butanal and 3 methyl-butanol γ-n-caprolactone, pentofuran), depending on genotype and year. A higher ratio of saturated fatty acids negatively influenced the flavour and odour characteristics. In the headspace volatiles, these features correlated negatively with 2-pentylfuran and hexanal. The oil content of poppy flour has a positive effect on colour, appearance, tactility and poppy flavour. Our results support a goal-oriented use of poppy genotypes for high-quality dietary products.