Within a generic model we analyze the Stokes linewidth in surface enhanced Raman scattering (SERS) from molecules embedded as bridges in molecular junctions. We identify four main contributions to the off-resonant Stokes signal and show that under zero voltage bias (a situation pertaining also to standard SERS experiments) and at low bias junctions only one of these contributions is pronounced. The linewidth of this component is determined by the molecular vibrational relaxation rate, which is dominated by interactions with the essentially bosonic thermal environment when the relevant molecular electronic energy is far from the metal(s) Fermi energy(ies). It increases when the molecular electronic level is close to the metal Fermi level so that an additional vibrational relaxation channel due to electron-hole (eh) exciton in the molecule opens. Other contributions to the Raman signal, of considerably broader linewidths, can become important at larger junction bias.