Far-infrared diagonal and Hall conductivities of multilayer epitaxial graphene on the C face of SiC were measured using magneto-optical absorption and Faraday rotation in magnetic fields up to 7 T and temperatures between 5 and 300 K. Multiple components were identified in the spectra, including (i) a quasiclassical cyclotron resonance, originating from the highly doped graphene layer closest to SiC, (ii) transitions between low-index Landau levels (LLs), which stem from weakly doped layers, and (iii) a broad optical absorption background. Electron- and hole-type LL transitions are optically distinguished and shown to coexist. An electron-hole asymmetry of the Fermi velocity of about 2% was found within one graphene layer, while the Fermi velocity varies by about 10% across the layers. The optical intensity of the LL transitions is several times smaller than is theoretically expected for isolated graphene monolayers without electron-electron and electron-phonon interactions.