Isomeric states (Isomers) in odd-odd (120)I (122)I, (124)I nuclei have been investigated using in-beam gamma-ray spectroscopy with the (118)Sn((6)Li,4n), (120)Sn((7)Li,5n), and (122)Sn((7)Li,(5)n) reactions at E(lab) = 48, 58, and 54 MeV, respectively. Several isomers with half-lives ranging from a few nanoseconds to tens of microseconds have been identified for the first time and the absolute excited energies have been established by linking the low- and high-spin levels through the feeding and decay of the isomers in these nuclei. The properties of the isomers have been discussed in terms of spin traps and high-K isomerism based on two-quasiparticle configurations. The systematics for the absolute excitation energies of the J(pi) = 7(-) and 8(-) high-K isomers based on the pi g(9/2)circle times vh(11/2) configuration are presented for (116)I to (124)I and compared with the 9/2(+) states in the neighboring odd-A I isotopes.