Excited states in 58, 60, 62Ni were populated via inelastic proton scattering at the Australian National University as well as via inelastic neutron scattering at the University of Kentucky Accelerator Laboratory. The Super-e electron spectrometer and the CAESAR Compton-suppressed HPGe array were used in complementary experiments to measure conversion coefficients and δ(E2/M1) mixing ratios, respectively, for a number of 2+ → 2+ transitions. The data obtained were combined with lifetimes and branching ratios to determine E0, M1, and E2 transition strengths between 2+ states. The E0 transition strengths between 0+ states were measured using internal conversion electron spectroscopy and compare well to previous results from internal pair formation spectroscopy. The E0 transition strengths between the lowest-lying 2+ states were found to be consistently large for the isotopes studied.