Also note that on lower resistance settings on multimeters, typically the higher the voltage on the leads. Use the 100-ohm setting for diodes if the meter does not have a diode checker setting.
This oscillator needs to run from a DC supply at a set voltage, but will run from 5V up to 15V DC no problem, and won't require much power, probably 250mA at the most steady-state. The rail power can be "whatever" it needs, and the high voltage will simply "ride" on top of it.
Good luck. These things are tough without a few other tools to support you, like a multimeter with a diode tester, or even better, a cheap oscilloscope.