Strong L-shell x-ray emission has been obtained from Kr clusters formed in gas jets and irradiated by 60-500-fs laser pulses. Spectral lines from the F-, Ne- Na-, and Mg-like charge states of Kr have been identified from highly resolved x-ray spectra. Spectral line intensities are used in conjunction with a detailed time-dependent collisional-radiative model to diagnose the electron distribution functions of plasmas formed in various gas jet nozzles with various laser pulse durations. It is shown that L-shell spectra formed by relatively long nanosecond-laser pulses can be well described by a steady-state model without hot electrons when opacity effects are included. In contrast, adequate modeling of L-shell spectra from highly transient and inhomogeneous femtosecond-laser plasmas requires including the influence of hot electrons. It is shown that femtosecond-laser interaction with gas jets from conical nozzles produces plasmas with higher ionization balances than plasmas formed by gas jets from Laval nozzles, in agreement with previous work for femtosecond laser interaction with Ar clusters.