High angular momentum states in odd-odd ${}^{86}\mathrm{Nb}$ were populated through the ${}^{58}\mathrm{Ni}{(}^{32}\mathrm{S},3pn)$ reaction at 135 MeV. Recoiling ${}^{86}\mathrm{Nb}$ nuclei were stopped in a thick Ta backing. Prompt multi-$\ensuremath{\gamma}$ coincidences with evaporated charged particles were detected using the full array of Gammasphere and the Microball. Mean lifetimes of 51 levels in ${}^{86}\mathrm{Nb}$ were measured using the Doppler-shift attenuation method. Strongly alternating magnetic dipole transition strengths were observed in the yrast positive-parity bands. Most of the transition quadrupole moments inferred from the lifetimes lie in the range of 1 to $2.7 e\mathrm{b},$ which would correspond to quadrupole deformations ${\ensuremath{\beta}}_{2}$ of 0.10 to 0.27 in a rotational model. Comparison with Hartree-Fock-Bogoliubov cranking calculations suggests triaxial to oblate shapes.