Infrared spectroscopic observations have established the presence of solid methanol (CH3OH) in the interstellar medium and in solar system ices, but the abundance of frozen CH3OH cannot be deduced without accurate band strengths, optical constants, and reference spectra. In this paper we identify disagreements, omissions, and gaps in the literature on infrared (IR) intensities of methanol ices, including unaddressed concerns that reach back several decades. New spectra are presented with intensity measurements aided by new data on the index of refraction and density of solid CH3OH. The result is that the large discordant results from different laboratory groups can now be reconciled. Multiple ices have been used to determine, apparently for the first time, IR intensities of H2O + CH3OH mixtures of accurately known composition for use with observations of interstellar ices. Also for the first time, measurements on CH3OH ices with different thicknesses have allowed us to report both near-IR band strengths and optical constants for two near-IR features used by planetary scientists. We have used our new IR results to determine vapor pressures of solid CH3OH and have compared them to measurements made with a quartz-crystal microbalance. Thermal annealings of methanol ices have been carried out and phase changes in the solid state examined. Comparisons of our results to earlier work are presented where possible, and electronic versions of our new results are made available.