Play between axle and bearing inner ring Got new 'low' cost wheels with noticeable rattling in both of them. Thought cartridge bearings had an excessive play. Turns out there is some play between bearing inner ring and axle.

Lock nuts were quite tight. After undoing the non-drive side nuts and and tightening them finger tight the play disappears. After tightening the quick release skewer the wheel seems like it's not turning freely enough.

Then after tightening the round nut against the lock nut when the skewer is tightened everything seems fine, but after removing the wheel lock nut is completely loose. Could it be due to loose low quality threads on round nut and lock nut?

Don't have much experience with cartridge bearing hubs as I got these due to partially cracked rims on old wheels and was tired of adjusting the cup and cone type ones.

Probably some of them have bearing sleeves like these (the picture is unintelligible).

Regarding to bearing preload, don't know why spring loaded bearings like these aren't used in bicycle hubs.
I know this type of hubs a Open Bearing hubs. You can have a "basket", a sort of ring that holds the ball bearings in position, and just ball bearings sticked with grease.

The way the axle sits on them, fully asambled should be like, from left to right: LockNut(quick release if you have one),dropout,Counter-Nut, Cone,hub, Cone, Counternut, dropout, locknut.

So, your problem is that you have play, but when you mount the wheel it goes stiff. 

For this problem you have to tight the CounterNut and Cone, together on one side. Then tight the other cone, just enough so you don't have play and runs smooth. Grab a thin wrench, if you have a cone wrench will be better, hold the cone with it and then with a second wrench tight the counternut.

Don't overtight the nuts, as a cheap axle is really easy to stripe. If the nuts keep loosing themselves get some preassure washers(the spiky ones) and put one beteween the cone and the washer.

cheers.

EDIT: Probably the black thing is just a dust seal, which makes seem like a sealed bearing.