The masses and pole residues of the ground and first radially excited Omega(0)(c) states with spin-parities J(P) = 1/2(+), 3/2(+), as well as P-wave Omega(0)(c) with J(P) = 1/2(-), 3/27(-) are calculated by means of the two-point QCD sum rules. The strong decays of Omega(0)(c) baryons are also studied and the widths of these decay channels are computed. The relevant computations are performed in the context of the full QCD sum rules on the light cone. The results obtained for the masses and widths are confronted with recent experimental data of the LHCb Collaboration, which allow us to interpret Omega(c)(3000)(0), Omega(c)(3050)(0), and Omega(c)(3119)(0) as the excited css baryons with the quantum numbers (1P, 1/2(-)), (1P, 3/2(-)), and (2S, 3/2(+)), respectively. The (2S, 1/2(+)) state can be assigned either to the Omega(c)(3066)(0) state or the Omega(c)(3090)(0) excited baryon.