We present a study of excited charm-strange baryon states produced in e(+)e(-) annihilations at or near a center-of-mass energy of 10.58 GeV, in a data sample with an integrated luminosity of 384 fb(-1) recorded with the BABAR detector at the PEP-II e(+)e(-) storage rings at the Stanford Linear Accelerator Center. We study strong decays of charm-strange baryons to Lambda K-+(c)S(0), Lambda K-+(c)-, Lambda K-+(c)-pi(+), Lambda K-+(c)S(0)pi(-), Lambda K-+(c)S(0)pi(-)pi(+), and Lambda K-+(c)-pi(+)pi(-). This study confirms the existence of the states Xi(c)(2980)(+), Xi(c)(3077)(+), and Xi(c)(3077)(0), with a more accurate determination of the Xi(c)(2980)(+) mass and width. We also present evidence for two new states, Xi(c)(3055)(+) and Xi(c)(3123)(+), decaying through the intermediate-resonant modes Sigma(c)(2455)K-++(-) and Sigma(c)(2520)K-++(-), respectively. For each of these baryons, we measure the yield in each final state, determine the statistical significance, and calculate the product of the production cross section and branching fractions. We also measure the masses and widths of these excited charm-strange baryons.