Think that problem is the UV's.

Whats happening is that when your painting the strokes your actualy painting the strokes positions based on the UV's, if youve modeled and then painted your UV's will be overlapping hence the problem. UV map then paint the strokes (as the way I think of it its part of texturing).

If you open the UV editor it propable will look like a jumbeled mess, thats the problem, lay out the UV's (either auto map or go the full hog and do the full lot) andthen give it a go.

Hope it helps