Amplification of soft x rays in Sr (Z=38) plasmas produced by second-harmonic laser irradiation of exploding foil targets is studied. Gains of 4.4 and 4.0 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively, have been measured for the 164.1- and 166.5-\AA{} J=2 to 1 transitions in Ne-like Sr at laser intensities of 1.3\ifmmode\times\else\texttimes\fi{}${10}^{14}$ W/${\mathrm{cm}}^{2}$. Numerous x-ray and soft-x-ray transitions were identified in order to demonstrate typical spectra from x-ray laser plasmas and infer information regarding the plasma ionization balance. The J=0 to 1 transition at 159.8 \AA{}, analogous to the well-known Se J=0 to 1 line at 182.4 \AA{}, was not definitively observed due to a wavelength overlap with a Na-like Sr line. Two other J=0 to 1 transitions of interest at 84.9 and 133.0 \AA{} were not observed. Reduced gain on the J=2 to 1 lasing lines was seen for several shots taken at a lower pump laser intensity of 7.0\ifmmode\times\else\texttimes\fi{}${10}^{13}$ W/${\mathrm{cm}}^{2}$. Possible reasons for this are considered. The results of this work imply the feasibility of a high-output-power cavity geometry Ne-like Sr x-ray laser operating at 164.1 and 166.5 \AA{}.