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 νμ and ν¯μ events we construct confidence intervals in two analysis spaces: sin2(2θ24) vs Δm412 under the conservative assumption θ34=0; and sin2(2θ24) vs sin2(2θ34) given sufficiently large Δm412 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.