We report measurements of charmonia produced in two-photon collisions and decaying to four-meson final states, where the meson is either a charged pion or a charged kaon. The analysis is based on a 395 fb(-1) data sample accumulated with the Belle detector at the KEKB electron-positron collider. We observe signals for the three C-even charmonia eta(c)(1S), chi(c0)(1P) and chi(c2)(1P) in the pi(+) pi(-) pi(+) pi(-), K+ K- pi(+) pi(-) and K+ K- K+ K- decay modes. No clear signals for eta(c)(2S) production are found in these decay modes. We have also studied resonant structures in charmonium decays to two-body intermediate meson resonances. We report the products of the two-photon decay width and the branching fractions, Gamma B-gamma gamma, for each of the charmonium decay modes.