Nitrogen (N) and sulfur (S) fertilization significantly affect seed yield and quality in Brassica oilseed crops. The effect of N and S management on the crop parameters (plant height, stem-base diameter, and number of branches), yield (seed yield components, seed and straw yields, harvest index—HI), and the quality of the seeds and oil (crude fat—CF, total protein—TP, crude fiber—CFR, fatty acids profile—FA, acid detergent fiber; and neutral detergent fiber) of oilseed radish (Raphanus sativus L. var. oleiformis Pers.) was analyzed in the study. The effect of N and S fertilization was evaluated in a field experiment in Bałcyny (north-eastern Poland) in 2020–2022. The experiment had a split-plot design with two factors and three replications. The first factor was the N rate (0, 30, 60, 90, 120 kg ha−1) and the second factor was the S rate (0, 15, 30 kg ha−1). Nitrogen fertilization stimulated stem elongation and branching. The average oilseed radish (OSR) seed yield ranged from 0.59 to 1.15–1.25 Mg ha−1. Seed yields increased significantly, up to 90 kg N ha−1 and 15 kg S ha−1. The N fertilizer use efficiency (NFUE) of OSR decreased with a rise in the N rate (from 4.22 to 2.19 kg of seeds per 1 kg N). The application of S did not increase NFUE. The HI ranged from 10% (0–30 kg N ha−1) to 12% (60 kg N ha−1). The contents of CF, TP, and CFR in OSR seeds (kg−1 dry matter—DM) were 383–384 g, 244–249 g, and 97–103 g, respectively. Nitrogen fertilization decreased the CF content (by 5%) and increased the contents of TP (by 5%) and CFR (by 16%) in OSR seeds. Sulfur fertilizer applied at 30 kg ha−1 decreased the CF content (by 2%), but it did not alter the content of TP or CFR. Oilseed radish oil contained 68–70% of monounsaturated FAs (MUFAs) (erucic acid accounted for 2/3 of the total MUFAs), 24–25% of polyunsaturated FAs (PUFAs), and 6–8% of saturated FAs (SFAs). Nitrogen fertilization increased the proportions of SFAs and PUFAs in OSR oil. Nitrogen rates of 60–90 kg ha−1 increased the contents of alpha-tocopherol (α-T), beta-tocopherol (β-T), and gamma-tocopherol (γ-T) in OSR seeds by 32%, 40%, and 27%, respectively. Sulfur fertilization increased the content of PUFAs and decreased the content of MUFAs in OSR oil, while it increased the contents of α-T (by 15%) and γ-T (by 19%) in OSR seeds. Proper N and S management in OSR cultivation can improve crop productivity and the processing suitability of seeds.