This page is dedicated to Math in Houdini, specifically using vex to manipulate things in 3d.
Quaternions:
I believe the best way to use quaternions is to understand what the Houdini quat functions are for. Understanding how to use the functions will provide good art direction for quaternions.
Also, with the two functions “maketransform” and “qconvert” you can convert between normal matrices and quaternions. A good workflow could be doing all your work on matrices, then converting them to quaternions at the very end.