We report in detail on searches for eV-scale sterile neutrinos, in the context of a (3+1) model, using eight years of data from the IceCube Neutrino Telescope. By analyzing the reconstructed energies and zenith angles of 305,735 atmospheric ({\nu }{\mu }) and ({\overline{\nu }}{\mu }) events we construct confidence intervals in two analysis spaces: ({\mathrm{sin}}^{2}\left(2{\theta }{24}\right)) vs (\Delta {m}{41}^{2}) under the conservative assumption ({\theta }{34}=0); and ({\mathrm{sin}}^{2}\left(2{\theta }{24}\right)) vs ({\mathrm{sin}}^{2}\left(2{\theta }{34}\right)) given sufficiently large (\Delta {m}{41}^{2}) that fast oscillation features are unresolvable. Detailed discussions of the event selection, systematic uncertainties, and fitting procedures are presented. No strong evidence for sterile neutrinos is found, and the best-fit likelihood is consistent with the no sterile neutrino hypothesis with a (p) value of 8% in the first analysis space and 19% in the second.