I've Googled this extensively and found conflicting information. The two bikes of my specific concern are an Electra cruiser (7-speed solid axle rear and solid front axle) and an Electra Townie (Modern [Shimano?] rear threaded COASTER BRAKE axle).

Most sites are in agreement that the font axles will all be 5/16" x 26 TPI, although I've seen some that said 9mm (without specifying a thread pitch).

Sites differ significantly about the rear axle threading.

Some say ⅜" x 26 TPI, others say ⅜" x 24 TPI, and some say 10mm metric (without specifying a thread pitch).

Since I don't have a thread gauge, does anyone know what this threading will be? Note that there are TWO rear axles of interest - the 7-speed and the coaster brake.

I understand that the Sturmy-Archer coaster brakes may (or may not) have a different axle than the Oriental ones. The SA models are of only academic interest to me at this time.

Thanks kindly - FH

There are a bunch of both Metric and English threaded axles available. 10mm, 9.5mm, 9 mm, 3/8 inch, 5/16 inch, are just a few. There are no standards except what the manufacturer of the hub decides to use. Sturmey Archers are another story because they until bought a few years ago used a thread called Whitworth that was only used by the British. There is no answer to your question. You can buy a digital caliper and Metric and English thread guage for under $20 and have the correct answers. Roger

Regarding modern Shimano 7-speed hubs, IGH will be 3/8x26 derailleur will be M10x1. Can you find part numbers on any of the hubs?

Metric axles are 1mm pitch.

The only hubs I've encountered with 3/8 x 24 threading are single speed coaster brake hubs. Can't remember what brand at the moment.
I have not seen 5/16" axles on any bikes built in recent times. Back in the days of 27" wheels, 5/16" fronts were common. Solid fronts will either be 3/8 x 26 or M9x1 in my experience.
According to this, Sturmey Archer has made the switch to metric for their new line of single speed coaster brake hubs.
https://www.sturmey-archer.com/files/...ER%20BRAKE.pdf
It shows axle diameter as M10. In the past, all hollow axle Sturmey gearhubs had 13/32" axles. The rotary 3 speeds were 3/8 x 26.

I use these both at home and at work and recommend them without reservation: The Original Thread Checker - Bolt, Screw, & Nut Identification Tool!
They are nice because they check both inside and outside threads.

Be wary of 10mm sizes, there are 3 different thread pitches, 1.0, 1.25 and 1.5mm

FWIW, The Taiwan based Run Race , is Now the owner and manufacturing company making sturmey archer products ..

sometimes they may still use the British machine tools & standards for retro compatibility..

Yes, Machine Shops Use a Thread pitch Gage, to answer these sorts of questions. by visual match.

All of the 10 mm rear axles I've dealt with are 1.0 mm thread pitch.

I ran into this problem when I wanted to convert two of my bikes to solid axles. It was pretty much an aesthetic pursuit, because I honestly couldn't say that there was anything wrong with the QR's. I ordered two 9x1 mm axles made by Wheels Manufacturing:

Wheels Manufacturing Hub Axles

My expectation was to switch my old cones to the new axles. Bike #1 , the cones wouldn't fit. I asked here, and learned that there are two 9 mm diameter threads. I tried Bike #2 , and the cones fit. The difference was probably European and Japanese, so I dug up another old Japanese hub and harvested its cones. In the end, everything fits.

An older Schwinn hub in my bin has the 5/16" axle.

A note about identifying the thread, 26 tpi is very close to 1 mm (25.4 tpi), so it might be hard to actually notice the difference unless you engage the nut or thread checker with several threads. Indeed, my 26 tpi cone went a few turns onto the 1 mm pitch axle before grinding to a halt, and the jam nut went on just fine. I may even have checked the threads with a jam nut before ordering the axles.

I'm guessing that the weird mixed English / metric threads arose from the availability of lathes and screw machines with English threading gears. Such a machine would let you chase English threads onto any diameter shaft, but metric threading required purchase of an additional set of gears. To this day, machinists will grumble if I ask for metric threads on a lathe job, which typically only crops up if I need a large fine pitch for some kind of lens or optical mount. Of course with taps and dies, no problem. But notice that 9x1 is not a widespread metric screw thread size.

Well, my specific questions regarding the three Electra bikes were answered by e-mailing Electra directly. Their reply:

Thank you for choosing Electra Bicycles, I hope all is well. I copied the axles specs below. I hope this helps, ride safe!

Townie 1 Front: M9 Rear: 9.5mm (3/8”) x 24 Tpi
Townie 3i Front M9 Rear: 9.5mm (3/8”) x 26 Tpi
Cruiser 7D Lux Front: 9.5mm (3/8”) x 26 Tpi Rear: 9.5mm (3/8”) x 26 Tpi

So, for threaded axles, everything BUT the coaster brake is ⅜ x 26 and the coaster itself is ⅜ x 24. I don't care about the M9s because they're already quick-release.

FH

Lowend fixies sometimes have 10mm solid front axles also.