  In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of
multi-dimensionally consistent difference equations (except Q4) were derived
using connection between the Q3 equation and the NQC equations, and then by
reductions. In that work central role was played by a Cauchy matrix. In this
work we use a different approach, we derive the $N$-soliton solutions following
Hirota's direct and constructive method. This leads to Casoratians and bilinear
difference equations. We give here details for the H-series of equations and
for Q1; the results for Q3 have been given earlier.
