which side did you connect the 120VAC to ?
I dont know this specific power. There should be a current limiter at .3A, which is suitable for high power LEDs.There can be 4 or 5 in series.Without a schematic, it difficult to tell how this one works. There may be some kind of PWM that explains your 'funny' reading.Try with a scope..
With a 400v rated capacitor onboard it is almost certain to be a switched mode power supply. Your best bet is to cut your losses, through the heap of junk away and buy a decent supply rated to do what you wish.
It has 70 v AC on the output side ? If that is what you mean, it sounds dangerous.It is strange that the ad for that device doesn't mention the output voltage or current at all, it's impossible to understand from the ad what you could actually use it for.
This power supply is meant to supply a current of 300mA to a string of 4 or 5 LEDs in series. Under these conditions the output voltage will be up to around 16V.If you connect a different load then things will change. It will try it's best to deliver a current of 300mA, (that is what it is designed to do), and the voltage will increase or decrease as appropriate to maintain that current.If your load is a 9V battery, then a current of 300mA can flow and the voltage will be a little over 9V. I would expect the battery to get hot after a while.However if your load is a 7805 voltage regulator powering an Arduino, that only requires a current of around 50-100mA when powered correctly, then the only way the power supply can try and deliver that 300mA is to raise the output voltage as high as it can. You are lucky that the 7805 hasn't failed and allowed a high voltage to damage your Arduino.