In the first paper of the present series, we proved the standardness of subgroups containing a split maximal torus in the split orthogonal group SO(n, R) over a commutative semilocal ring R for the following two situations: 1) n is even; 2) n is odd and R = K is a field. In the present paper, we prove the standardness of intermediate subgroups over a semilocal ring R in the case of an odd n. Together with the preceding papers by Z. I. Borewicz, the author, and E. V. Dybkova, this paper completes the description of the overgroups of split maximal tori in the classical groups over semilocal rings. The analysis of odd orthogonal groups turned out to be technically much more difficult than other classical cases. Unlike all preceding papers, the proof of the key step in the reduction to the case of a field relies on calculations in a class of semisimple elements that are neither microweight elements nor semisimple root elements.