The oxyselenide $\mathrm{K}{\mathrm{V}}_{2}\mathrm{S}{\mathrm{e}}_{2}\mathrm{O}$, featuring an anti-${\mathrm{K}}_{2}\mathrm{Ni}{\mathrm{F}}_{4}$-type layered structure, was successfully synthesized using a self-flux method. Comprehensive structural, electrical, and heat transport, as well as magnetism measurements, were performed on both single crystals and polycrystals. At 105 K, a density-wave (DW)-like anomalous transition is revealed in temperature-dependent resistivity and Hall coefficient, signifying possibly the opening of DW gaps. This transition is also confirmed by the temperature dependence of magnetic susceptibility and specific heat as a second-order transition. No superstructural peaks and peak splitting were observed in the conventional x-ray diffraction spectra, indicating either a rather small distortion amplitude or a more complicated mechanism than charge- or spin-density waves. Additionally, measurements on the magnetotransport properties of $\mathrm{K}{\mathrm{V}}_{2}\mathrm{S}{\mathrm{e}}_{2}\mathrm{O}$ single crystals under a magnetic field up to 16 T have been conducted. Clear Shubnikov--de Haas (SdH) oscillations are observed, and parameters of the Fermi surface (FS), such as Fermi vector and effective mass, are calculated. Multiple FS sheets contribute to the SdH oscillations with frequencies ${F}_{\ensuremath{\alpha}}=5\phantom{\rule{0.16em}{0ex}}\mathrm{T}, {F}_{\ensuremath{\delta}}=62\phantom{\rule{0.16em}{0ex}}\mathrm{T}, {F}_{\ensuremath{\beta}}=220\phantom{\rule{0.16em}{0ex}}\mathrm{T}, {F}_{\ensuremath{\gamma}}=364\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, and ${F}_{\ensuremath{\eta}}=586\phantom{\rule{0.16em}{0ex}}\mathrm{T}$, respectively. Among them, ${F}_{\ensuremath{\alpha}}$ corresponds to a very small FS area and cyclotron effective mass, which is expected for Dirac or Weyl points. Beyond the quantum limit of \ensuremath{\alpha}-FS, an observation of negative magnetoresistance is noted. A linear fit to the Landau level fan diagrams yields values of Berry phase 0.97\ensuremath{\pi} (1.17\ensuremath{\pi}) for ${F}_{\ensuremath{\alpha}}$ (${F}_{\ensuremath{\beta}}$), indicating the existence of nontrivial band structures in $\mathrm{K}{\mathrm{V}}_{2}\mathrm{S}{\mathrm{e}}_{2}\mathrm{O}$.