Most of those look like axis light that is very expertly balanced with the ambient, either the lights on the street or a cafe, or the overcast sky.
Axis light can be very beautiful if used correctly. In fact, most of the time you shouldn't really notice it, such as in the first image outdoors with the feather hat. If your ambient light is f8, and you set the strobe to give you one to two stops less light, you get a very subtle fill and sparkle (especially with dark fabrics) that is very hard to spot. It's much like toning, it can be so subtle that without a comparison print, you wouldn't be able to tell. In the case of that image, it will also serve to keep the eyes from going "raccoon." Zoom in and look at the very soft shadow under the chin; open shade would not give you that look.
A great thing to do is find some overcast light, shoot one without flash, then add in balanced, one stop under and two stops under. So if your ambient is f11, then set the flash to give you f11, f8 and f5.6. Compare these frames. You'll find balanced flash is generally kind of ugly, one stop under is getting nice, but still noticeable, and two stops under will give you just a subtle lift and a touch of sparkle in the eyes. It's best if the flash is in fact right above the lens rather than to the side.
Same thing indoors. You need an ambient exposure where you really feel the lamps, such as in the fourth image; look at the hair and how it is a touch over exposed; that's what I mean by feeling it. Say that is 1/2 second at f5.6, your flash can be at f4 and you should be right on.
If you learn how to use professional lighting, you will be better than most photographers by a mile.
(By the way, this has been my 400th post!)