The feeding and decay patterns of isomers in odd-odd iodine nuclei, produced in heavy-ion fusion-evaporation reactions and separated by a recoil mass spectrometer, have been studied with the \ensuremath{\gamma}-ray spectroscopy technique. A new isomer in $^{116}\mathrm{I}$, fed by a known collective band, was identified and its half-life was measured to be 3.27\ifmmode\pm\else\textpm\fi{}0.16 \ensuremath{\mu}s. An isomer was confirmed to exist in $^{122}\mathrm{I}$ with a measured half-life of 80\ifmmode\pm\else\textpm\fi{}8 \ensuremath{\mu}s in agreement with two previous determinations. It is established from our study that these isomers serve as links between the high-spin and low-spin states in $^{116,122}\mathrm{I}$. The characteristic properties of low excitation energy and high spin of these isomers are evident. As a by-product in the study of $^{122}\mathrm{I}$, the half-life of a known high-spin isomer in $^{121}\mathrm{I}$ was measured to be 16.0\ifmmode\pm\else\textpm\fi{}1.4 \ensuremath{\mu}s, which disagrees with an early measurement of 9.0\ifmmode\pm\else\textpm\fi{}1.5 \ensuremath{\mu}s. Its isomeric transition has an energy of 135 keV as suggested by our data in contrast to the value of 159 keV reported earlier.