Multielectron ionization and Coulomb explosion of methane clusters (CA(4))(n), A = H, D, and T, in very intense (I = 10(18)-10(19) W cm(-2)) laser fields were studied using classical dynamics simulations. The products of Coulomb explosion involve light A(+) ions (p, d, and t nuclei) with energies up to 20 keV, C4+ ions at I = 1018 W cm(-2), and C6+ ions (carbon nuclei) with energies up to 110 keV at I = 1019 W cm(-2). Important advantages of nuclear fusion driven by Coulomb explosion of methane (C(4+)A(4)(+))(n) and (C(6+)A(4)(+))(n), heteronuclear clusters pertain to energetic effects, with the heavy multielectron ions driving the light H+, D+, or T+ ions (d or t nuclei) to considerably higher energies than for homonuclear deuterium clusters of the same size, and to kinematic effects, which result in a sharp high-energy maximum in the light-ion spectrum for the (C(4+)A(4)(+))(n) and(C6 A(4)(+)), clusters. We studied the energetics of Coulomb explosion in conjunction with isotope effects on the product A(+) and Ck(+) ions energies and established the cluster size dependence of dd and dt fusion reaction yields from an assembly of Coulomb-exploding clusters. The C6+ nuclei produced by Coulomb explosion of (C6+D4+)(n) (n 5425) clusters are characterized by an average energy of E-av = 65.2 keV and a maximum energy of E-M 112 keV. A. search was undertaken for the C-12(6+) + H-1(+) fusion reaction of astrophysical interest.