...However I also read somewhere that the designers used slide rulers to calculate all the stresses and strains at different conceivable flight loadings.

Slide rules, mechanical calculators (what the older of us might call an "adding machine"), and good old paper and pencil.

This interested me the most because I'm not at all familiar with how such conceivable flight situations are defined and then how someone might go about calculating the forces given the tiny pieces that these things are built from.

Same way you eat an elephant: One bit at a time. Rigid airships are basically giant 3D trusses that are built of smaller trusses. You calculate the loads on each large fin, control surface, and the entire big truss for the entire airship, finding the loads in each "strut" that makes up the big truss. Then once you have the load in that member, you calculate the load inside the smaller truss that makes it up, and down and down until you get to the smallest pieces. They accomplished that with rows and rows of "calculators": People at desks whose job it was to run stresses on their little part(s) of the structure.

I'm sure they probably established "standard" truss members that could take pre-defined loadings, and didn't analyze every single little strut making up each section of truss. That would save a lot of time and effort, and if they had several "standard" units, wouldn't result in much of a weight penalty.

We tend to think of such things being impossible without digital computers, but the computer is just doing the same ultimate task, much faster and with fewer people. In the end, it's all just math. You could design the structure of an F-22 with paper and pencil and a pocket calculator, if you had enough time.