We present an efficient transfer matrix formalism for obtaining the quantum conductivity of single-wall carbon nanotubes (SWCN's) based on a nonorthogonal tight-binding scheme. The formalism is used to calculate conductivity in the presence of topological defects and H adsorbates. I-V characteristics show large oscillatory behavior as a function of the number of H adatoms for both (10,0) and (5,5) SWCN's. Furthermore, the conductivity is found to depend sensitively on structural relaxation.