Insulation thickness varies with the specs that the wires are rated at and the insulation type. The copper wireinside is made up of strands of smaller wire. They typically start with 7 strands, one wire in the center with six wires surrounding it. Flexible wire is going to have at least 49 strands with it going up from there. The wire size and space between wires plays a role in the actual coper density or cross sectional are. This can be measured in two axis to give mm2 (squared millimeters) or expressed as a decimal reading in inches squared.
American Wire Gauge (AWG) is used in the USA but most countries in other parts of the world go by mm2 measurement.
I am not sure how you really can measure it accurately.
Lots of commonly found wire strippers are designed for solid wire, this is why you end up cutting some strands of very high count stranded wire. Most of the time it is not going to matter much losing a few wires of a stranded wire of over 100 wires. We aren't dealing with things requiring high tolerances.
Go to Wikipedia and read up on the stranded wires and insulation type and things like that if it suits your curiosity.
I don't know how to tell you to measure a wire if it isn't marked. Like you said, you can get close using the wire strippers starting large and working down to see which one cuts through the insulation without cutting the strands. Otherwise, you need the specs on the wire from the maker.
David