Abstract: Background: The mercury isotopes around N = 104 are a well-known example of nuclei exhibiting shape coex-istence. Mixing of configurations can be studied by measuring the monopole strength rho^2(E0), however, currently the experimental information is scarce and lacks precision, especially for the I^pi -> I^pi (I not = 0) transitions. Purpose: The goals of this study were to increase the precision of the known branching ratios and internal conversion coefficients, to increase the amount of available information regarding excited states in 182,184,186Hg, and to interpret the results in the framework of shape coexistence using different models. Method: The low-energy structures in 182,184,186Hg were populated in the & beta; decay of 182,184,186Tl, produced at ISOLDE, CERN and purified by laser ionization and mass separation. The & gamma;-ray and internal conversion electron events were detected by five germanium clover detectors and a segmented silicon detector, respectively, and correlated in time to build decay schemes.Results: In total, 193, 178, and 156 transitions, including 144, 140, and 108 observed for the first time in a & beta;-decay experiment, were assigned to 182,184,186Hg, respectively. Internal conversion coefficients were determined for 23 transitions, out of which 12 had an E0 component. Extracted branching ratios allowed the sign of the interference term in 182Hg as well as & rho;2(E 0; 0+2 & RARR; 0+1 ) and B(E2; 0+2 & RARR; 2+1 ) in 184Hg to be determined. By means of electron-electron coincidences, the 0+3 state was identified in 184Hg. The experimental results were qualitatively reproduced by five theoretical approaches, the interacting boson model with configuration mixing with two different parametrizations, the general Bohr Hamiltonian, the beyond mean-field model, and the symmetry-conserving configuration-mixing model. However, a quantitative description is lacking. Conclusions: The presence of shape coexistence in neutron-deficient mercury isotopes was confirmed and evidence for the phenomenon existing at higher energies was found. The new experimental results provide important spectroscopic input for future Coulomb excitation studies.