Excited states in odd-odd $^{70}\mathrm{Ga}$ were studied using the $^{62}\mathrm{Ni}(^{14}\mathrm{C},\ensuremath{\alpha}pn)$ fusion-evaporation reaction performed at the John D. Fox Superconducting Accelerator Facility at Florida State University with a beam energy of 50 MeV. The depopulating $\ensuremath{\gamma}$ decays were measured in coincidence using a Compton-suppressed Ge array consisting of three clover detectors and seven single-crystal detectors. An investigation of these coincidences resulted in the addition of 16 new transitions in the $^{70}\mathrm{Ga}$ level scheme, including some which belong to the onset of a new positive-parity band structure likely based on the $\ensuremath{\pi}{g}_{9/2}\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}$ configuration. Spins and parities were assigned based on directional correlation of oriented nuclei ratios and linear polarization measurements. The excitation energies predicted by shell-model calculations using the JUN45 effective interaction compare favorably with the experimental ones for the positive-parity states, but are generally about 400--500 keV too low for the negative-parity states. Total Routhian surface calculations for the lowest positive-parity configuration with signature $\ensuremath{\alpha}=0$ predict significant triaxiality $(\ensuremath{\gamma}\ensuremath{\approx}\ensuremath{-}{20}^{\ensuremath{\circ}})$ with competing noncollective excitations developing at a spin $(J=8)$ that corresponds to the onset of the positive-parity band observed experimentally. The calculations for the lowest negative-parity states with $\ensuremath{\alpha}=0$ yielded surfaces that were qualitatively similar.
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