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One of the key issues in unraveling the mystery of high T _C superconductivity in the cuprates is to understand the normal state outside the superconducting dome. Here we perform scanning tunneling microscopy and spectroscopy measurements on a heavily overdoped, non-superconducting (Bi, Pb) _2 Sr _2 CuO _6+ _δ cuprate. Spectroscopic imaging reveals dispersive quasiparticle interferences (QPIs) and the Fourier transforms uncover the evolution of momentum space topology. More interestingly, we observe nanoscale patches of static charge order with $\sqrt{2}\times \sqrt{2}$ periodicity. Both the dispersive QPI and static charge order can be qualitatively explained by theoretical calculations, which reveal the unique electronic structure of strongly overdoped cuprate.