You can get new single bearing balls at most hardware stores but I would get new cones and bearings from a seller like Niagaracycle.com. If you have some freewheel bike it will almost certainly be standard except for maybe the dust caps on the axle cones, which can be tapped off gently and changed out.
Roll the axle across a smooth tabletop. I bet you it's bent and wobbly.
You don't torque cone nuts down. you tighten the cone by hand against the bearing balls and maybe back off a few degrees, then tighten the locknut against the cone while holding the cone still with a special, thin wrench. The idea is to take out all the play but not tighten it any further.
Some people think you should give the cone a very slight preload; maybe 10 degrees after it touches the balls.
I also find it's necessary to readjust a few times in the first few miles as the cones break in. Cheap ones will not have a smooth finish and you will lose the initial adjustment as the cones break in.
Maybe get a book from the library or go to parktool.com for more info.