Local star-forming galaxies show properties that are thought to differ from galaxies in the early Universe. Among them, the ionizing stellar populations and the gas geometry make the recipes designed to derive chemical abundances from nebular emission lines to differ from those calibrated in the Local Universe. A sample of 1969 extreme emission-line galaxies (EELGs) at a redshift 0 ≲ z ≲ 0.49, selected from the Sloan Digital Sky Survey (SDSS) to be local analogues of high-redshift galaxies, was used to analyse their most prominent emission lines and to derive total oxygen abundances and nitrogen-to-oxygen ratios following the direct method in the ranges 7.7 < 12 + log(O/H) < 8.6 and -1.8 < log(N/O) < -0.8. They allow us to obtain new empirically calibrated strong-line methods and to evaluate other recipes based on photoionization models that can be later used for a chemical analysis of actively star-forming galaxies in very early stages of galaxy evolution. Our new relations are in agreement with others found for smaller samples of objects at higher redshifts. When compared with other relations calibrated in the local Universe, they differ when the employed strong-line ratio depends on the hardness of the ionizing radiation, such as O32 or Ne3O2, but they do not when the main dependence is on the ionization parameter, such as S23. In the case of strong-line ratios depending on [N II] lines, the derivation of O/H becomes very uncertain due to the very high N/O values derived in this sample, above all in the low-metallicity regime. Finally, we adapt the Bayesian-like code H II-chi-mistry for the conditions found in this kind of galaxies and we prove that it can be used to derive within errors both O/H and N/O, in consistency with the direct method.