Aims. We wish to improve the accuracy of oscillator strength values for several Ni ii UV transitions and measure for the first time the f-value of a few other weak transitions for which no laboratory nor astronomical measurement is presently available. Methods. Four quasars displaying five damped Lyman α systems with relatively strong Ni ii lines were selected. From the analysis of the excellent high resolution spectra available, we determined the relative f-value of Ni ii transitions by comparing the strength of the corresponding absorption profiles. To quantify the latter, we used the apparent optical depth method for resolved features, equivalent width measurements for optically thin lines and line fitting with VPFIT. Absolute f-values were then derived by relating our determinations to the available laboratory measurements. Results. Thanks to the good signal-to-noise ratio of the spectra and to the suitable properties of the absorption systems investigated, we are able to significantly improve the determination of the f-value for 13 Ni ii transitions falling in the 1317-1804 Å interval. Our results are found to be consistent with other earlier determinations for ten of these transitions; our median relative accuracy for these f-values is 6.5%. For three weak transitions near 1502, 1773, and 1804 Å, which have not been detected previously in astronomical spectra, we can get a first measurement of their f-value. Conclusions. Our work illustrates that, thanks to the redshift and the absence of variations of physical constants on cosmological scales, the analysis of absorption lines induced by remote gas in quasar spectra can nowadays provide valuable constraints on atomic data in the UV range.