Rear axle for Alexrims DC 4.5 Disc 26" MTB wheels w/ Formula hubs

If the hub has a smooth, straight-walled 12mm diameter hole through it, yes it's for a 12mm through axle. (A 'through axle' isn't really the axle of course, it's a fastener that goes through the hollow axle in the hub.)

If this is the case, there are through-axle to quick release adapters available that you can use.

BTW, have you checked that the hub width is correct for your frame?

UPDATE: Nope not through-axle. Just missing axle and bearings.

It's likely not going to be practical to fix this.

The axle is the easy part. It's a standard axle hub. You need any 146mm M10 quick release repair type axle.

The cones and seals are the problem. They have to be right for the hub. The main conceivable way of getting what you need is finding another of the same hub in a big nasty box at a used parts oriented shop. With some time and hassle, cones might be obtainable new or cannibalized if you both looked hard enough and were willing to do the work of obtaining and testing them, i.e. assembling the hub with them and seeing how you feel about where the ball track is falling. That still leaves seals. They're only going to come from a donor hub.

You need to look for explanations why it got parted from its guts to begin with. Are the cups in good enough shape to warrant messing with? Is the freehub working right?