We report in detail on searches for eV-scale sterile neutrinos, in the context of a 3 þ 1 model, using eight years of data from the IceCube Neutrino Telescope. By analyzing the reconstructed energies and zenith angles of 305,735 atmospheric ν μ andν μ events we construct confidence intervals in two analysis spaces: sin 2 ð2θ 24 Þ vs Δm 2 41 under the conservative assumption θ 34 ¼ 0; and sin 2 ð2θ 24 Þ vs sin 2 ð2θ 34 Þ given sufficiently large Δm 2 41 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.