We investigate equilibrium states, magnetic response and the normal oscillations of internal degrees of freedom (Higgs modes and Goldstone modes) of three-band superconductors accounting the terms of both internal proximity effect and the ``drag'' effect (intergradient interaction) in the Lagrangian. Both the Goldstone mode and the Higgs mode are split into three branches each: common mode oscillations and two modes of anti-phase oscillations, which are analogous to the Leggett mode in two-band superconductors. It is demonstrated that the second and third branches are nonphysical, and they can be removed by special choice of coefficients at the ``drag'' terms in Lagrangian. As a result, three-band superconductors are characterized by only single coherence length. Spectrum of the common mode Higgs oscillations has been obtained. The magnetic penetration depth is determined with densities of superconducting electrons in each band, although the drag terms renormalize the carrier masses.