The elements of the kits are a combination of made, purchased, and modified.

I've been using one of these for a week, keeping it in my purse and not being particularly careful with it. It's holding up well so far.

The pins are modern glass-headed pins; I've seen references to glass-headed pins, but didn't take the time to track them down for this project.
Hand-made needles very similar to those held by the Museum of London are available, but prohibitively expensive, and while I looked into making my own, I ran out of time and energy.

Cylindrical wood tubes were used as pin and needle cases on the Mary Rose, though those had stoppers, not caps, and had dividers so they could be used as thread-winders at the same time.
These were a batch of seconds, where the lid didn't fit tightly. I wrapped them with waxed thread to snug up the fit.

The wax hexagons are from a friend who keeps bees. To protect the wax from lint, and to protect the rest of the contents of the kit from wax, I wanted a little pouch to keep it in. A reusable/disposable tea bag was about the right size, so I copied it (tweaking the dimensions) out of a silk organza. I wanted a thin fabric that wouldn't add a lot of bulk, and I wanted a stiff fabric that wouldn't cling to the wax while inserting and removing it. I happened to have a remnant of rose-colored silk organza with an intact selvedge edge, which cut down on my narrow hems in disobedient fabric. (Silk organza is kind of a nightmare to work with)
clockwise from top left: inside out bag, right side out bag, wax, original tea bag.
Caution: when using a leather thimble, the eye end of the needle will eventually inevitably punch through and into your finger. This will hurt a lot when it happens, because it only happens when you're using a lot of force.
The tails are doubtless too long. Adjust to fit and trim as desired.

This type of springy shear was pretty common throughout period. I didn't notice until I was almost done inserting them into their sheathes that the "spring" part is actually plastic.
I apologize, but as I was fooled for a long time *with them in my hands,* I think they'll pass.
The leather sheath is just to keep the tips covered, for safety. The loop is meant for hanging.

Bone, modern. The awls are a very common Victorian design (though there's nothing about them that couldn't or necessarily even wouldn't have been done in period)
Thread winders
These are based sort of roughly off of a Viking find, and were a massive exercise (for me) in poor decision making.
Wood is not my medium. Therefore, I have not earned the right to take short cuts, even though I know there are shortcuts to be had.
They exist.
That's enough.
Other people's research and variations:
A Viking/Saxon Sewing Box
Putting Together A Medieval Sewing Kit