The comments Flux made above are appropriate for NiMH batteries, he's assuming you are considering using these although he doesn't spifically call it out.
Unfortunately the charge requirements of NiMH are non-trivial, NiCad on the other hand are much easier to charge although the technology is hard to get these days as Cadmium is nasty stuff and the charge density of NiMH is about twice as good.
Is the 0.4V coming off the wind generator for one coil or for all the coils in series? 0.4V is too low to do anything.
If it's one coil and you can get them all in series you might have enough power to do something but with no measurable current it's probably not enough to run the LED when you have wind, let alone also charge the batteries for when you don't.
A big capacitor might be a better choice than batteries as charging these is trivial (fit a zener diode in parallel to ensure you don't over voltage them and just connect across the cap, done).
To answer some of the questions you had in the footnotes:
Plugging into the utility is very complicated, it's not as simple as matching voltage, you need to match frequency and phase too and even then it's complicated.
Gauge of wire is important because current is limited by the thickness of the wire and resistance is decreased by thich wire. For these reasons you want thicker wire.
The number of windings governs the voltage, for this reason you want many turns of wire.
However the voltage and current is proportional to the gauss which is dependent on the proximity of the coil to the magnet. You therefore want the coil close to the magnet which drives fewer coils and thinner wire (to get the coils closer). This drives compromise in the design.
Working it out theoretically is far too complicated and involves too many unknows. Generally it's simpler to wind a test coil and see what happens.
Ideally the 'hole' in the coil is the same size as a magnet. YOu want one side of the coil to be passing over a N pole of a magnet as the other side of the coil passes of a S pole of the adjacent magnet.
Read:
http://www.sparweb.ca/2_Gen_Ax/AXIAL_FLUX_HowItWorks_V1a.pdf