A study of the ground states of the laser-ionized and mass-separated odd-odd isotopes Au180,182 was performed using the Resonance Ionization Laser Ion Source, Windmill detection setup and ISOLTRAP Multi-Reflection Time-of-Flight Mass Spectrometer at ISOLDE, CERN. A complex fine-structure α-decay pattern of Au180 was deduced, providing insight into the low-lying levels in the daughter nucleus Ir176. An α-decay branching ratio of bα(Au180)=0.58(10)% and a half-life of T1/2=7.2(5) s have also been derived, allowing for the calculation of the reduced α-decay widths and determining the degree of hindrance of respective α-decay branches. From complementary first in-source laser spectroscopy measurements of the hyperfine structure in atomic transitions of Au180,182, the nuclear magnetic moments of μ(Au180)=-0.83(9)μN and μ(Au182)=1.66(9)μN were extracted with an inclusion of a correction for the hyperfine anomaly. Based on the observed hyperfine structure patterns, and on the comparison of the measured and calculated μ values, a preferred ground-state spin and parity Iπ(Augs180)=(1+) is proposed, and the earlier assignment of Iπ(Augs182)=(2+) is confirmed. For Au180, the most probable proton-neutron Nilsson configuration of π3/2-[532] - ν5/2-[512] suggests the same proton state as in the heavier deformed odd-odd nuclei Au182,184.