Raspberry Pi losing power
If the power drops very quickly (which is the case when the servos start to move and you did not provide enough capacitance), you are not able to measure this (short) power drop with a standard multimeter. (according to this site, green LED is SDCARD access and does not monitor power). 

Solution: You need to provide (a lot) of capacitance (like e.g. 2x 470uF) to the servos. 

Best would be to have a seperate power supply for the servo and the pi.