Electrical – arduino/raspberry based current and voltage monitoring using Rogowski coil

Based off of your two specifications of

Battery powered (so all items must use minimum power)

WiFi enabled

I would recommend not going with an Arduino at all as it will be much more difficult to meet the minimum power requirement. In order to minimize your power you will need to look into spinning your own board with a very low power microcontroller. It seems like almost every microcontroller company sells some version of ultra low power, but the MSP430 seems to be the most widely used line for low power.

As far as the WiFi enabled part, this is a little bit more difficult to get to be low powered. If you are fine with having your device waking up to check in to see what it needs to do with the LED then you can get your power even lower. However, my guess is that you are actually wanting to be able to send your device a packet at any time to tell it to do something with the LED. In order to go this path with lowest power you would be best rolling your own WiFi solution, but my guess also is that you do not care to do this. So you will want to look for a module that will do this for you. Roving Networks has a few options that support 4uA sleep mode and 38mA active.

With all of that said, if you still want to go with an Arduino (even though you didn't say it was a requirement) you will have to settle for very poor battery life. By very poor battery life I mean something less then a day unless you want to lug around a car battery.

Your best bet is the conductive ink kind of sensor.

These are a little bit pricey but easy to get hold of. Sparkfun have them for $13.

They're pretty easy to use as they act just like a variable resistor, whose resistance changes as you bend it. You can make them into an analogue sensor by adding a fixed resistor. The impedance buffer (an op-amp) is optional, but will result in much better sensor readings, especially as you intend to use fairly long wires to connect the sensor to the Arduino.

The datasheet for the sensor (which you should read) contains lots more suggestions for circuits.

You can stitch a little pocket into clothing and insert the flex sensor. Use them in the fingers of a glove:

Or in a whole dress:

Added

Accuracy: Flex sensors aren't super accurate sensors. They give you a reasonable sense of an amount of bend, but aren't great for precision applications, E.G. robotic teleoperation. I don't know how much accuracy you need for the neck, so it's very hard for me to say whether it's good enough for you. If you want a more accurate sensor, you'll need to specify exactly how accurate.

Robustness: What will kill the sensor is not the angle of the bend, but the minimum bend radius.

The datasheet for the ones at Sparkfun didn't mention a minimum bend radius, but these ones specify 5mm. I.E. you can bend one around a 10mm diameter tube, and they'll be fine. So I would imagine that going round the outside of an elbow would be OK, but the inside would probably pinch the sensor and break it.