Excitation energies, term designations, and g factors of Th, Th+, and Th2+ are determined using a relativistic hybrid configuration-interaction (CI) plus all-order approach that combines configuration-interaction and linearized coupled-cluster methods. The results are compared with other theoretical and experimental values where available. We find some vanishing g factors, similar to those known in lanthanide spectra. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for Th2+. To estimate the uncertainties of our results, we compare our values with the available experimental lifetimes for higher 5f7p (3)G(4), 7s7p P-3(0), 7s7p P-3(1), and 6d7p F-3(4) levels of Th2+. These calculations provide a benchmark test of the CI plus all-order method for heavy systems with several valence electrons and yield recommended values for transition rates and lifetimes of Th2+.