One thing I do is unwrap sections of my mesh a section at a time, and I move that unwrapped part off to the side of the map and then hide that section of my mesh that I just unwrapped by pressing the H key after I've unwrapped it. That way I get that part of the map out of the way so I can unwrap the other parts. You can unhide it by pressing alt + H. Once I have everything unwrapped, then I start layering the sections that share a texture on top of each other--you can layer the undersides of your mesh right on top of the upper sides since the undersides won't show as much in the game.
Sometimes, to make things neater, I merge vertices (Press x and choose weld). Other times, if the unwrapped mesh is too curved, I straighten lines of vertices by highlighting all the vertices I want to straighten and either pressing S + X + 0, or S + Y + 0 depending on if the line I'm straightening is across the top or up and down.
Sometimes, as well, I'll unwrap a section by choosing Project From View. If you do this, you have to make sure the model is placed perfectly. You can choose front view (Numpad + 1), or back view (Ctrl + Numpad 1) or right or left side view (Numpad + 3 or Ctrl + Numpad 3, respectively). This way, I get a UV map section that is shaped the same as my mesh.
After I've layered everything I want to layer, straighten what I want straightened, merged vertices, etc., I start placing the parts on my UV map, arranging them as best I can. Since you're doing hair, I would imagine it's important to make sure your UV parts need to be placed up and down or you could end up with strange-looking textures. I'm not sure of that, however. I've never made hair, so don't quote me on this.
I just know I've had to do that with my Sims 3 object meshes so that patterns that are striped are all going the same direction on my mesh.
One other tip that I've found results in a less warped UV map when I unwrap my mesh is to first make sure my mesh is in object mode, then press Alt + A then choose Rotation & Scale. This makes the mesh unwrap in a nicer way.
Hope this helps! And the hair you made is super cute.
I just know I've had to do that with my Sims 3 object meshes so that patterns that are striped are all going the same direction on my mesh.