What to use for the axles?
The most important question to consider is whether the axle should rotate or should it be fixed. The other question is of course what material to use.
First, I used bamboo skewers. I glued them firmly to the legs and arms with hot glue. So these were rotating axles. (They rotate with the shoulders and with the hips within their holes.)

Bamboo skewers
Rotating bamboo skewer axles glued to the shoulder and hip. (This body is made of foam board.)
Later, I experimented with bicycle spokes as axles. They were stuck into cardboard channels and did not rotate. The arms and the legs were held together by traverses so they moved as one solid piece.
Bike spoke axles in cardboard channels. (Actually only one of the channels can be seen.) These are non rotating axles and can be pulled out easily. Only the friction keeps them in place. (The body is made of cardboard.)
In Barry's model, you can see, that the legs are held together by a traverse so they move as one piece but his arms are most likely move independently from each other. Well, he definitely uses two strings, one for each arm. If the arms move independently from each other, than the axle must be fixed (not rotating) and you must put some kind of stopper at the ends of the axle to prevent the shoulders falling off. I simplified this model by using traverses for the arms as well as for the legs. A traverse for the arms is tricky because you have to position it between the hands in such a way that it fits over the head. The simplest traverse is a piece of rectangular thin cardboard glued on the palms. It might not be the nicest, but easy to experiment with.
Cardboard traverse on the palms
Plywood traverses between the legs and hands are glued on. (The threaded rods (as axles) are in place for the gluing.)
Finally, I chose 3 mm threaded rods for the axles. Nuts with washers are tightened on the shoulders and hips.
So, connected by the traverse the two legs move as one solid piece and the axle rotates with them. The same is true of the arms.
I made my own little wrenches for tightening the washers. (Without them tightening the washers would be even more challenging. I guess you could buy such wrenches.)

Here is set from Conrad.