We report on the systematic evolution of normal-state properties and superconducting characteristics in filled-skutterudite compounds (Pr1−xLax)Os4Sb12 via Sb-NQR experiments. In the superconducting state for Pr-rich compounds, 1/T P r 1 exponentially decreases down to T = 0.7 K with no coherence peak below Tc as well as in PrOs4Sb12. A remarkable finding is that the residual density of states (RDOS) at the Fermi level below Tc is induced by La substitution for Pr. However, the RDOS does not increase and Tc does not decrease with increasing La content up to x = 0.2. These results are proposed to be understood in terms of a multiband-superconductivity model that assumes a full gap for part of the FS and an anisotropic gap for a small FS. The novel strong-coupling superconductivity in PrOs4Sb12 is inferred to be mediated by the local interaction between 4f2 -derived crystal-electric-field states with the electric quadrupole degree of freedom and conduction electrons. This coupling causes a mass enhancement of quasi-particles for a part of FS and induces a small FS. Note that the small FS does not play any primary role for the strong-coupling superconductivity in PrOs4Sb12.