Circuit for stabilizing the mini - 3 phase wind turbine output to 5 Volt using 7805 IC
A 3-phase machine produces AC:


  I am also curious that my cheap Multimeter (under $10) does not show any voltage out of the IC and of motor but works for AAA/AA etc.


Your multimeter is set to DC when it can measure the voltage of batteries. 

DC is not AC.

LEDs and the 7805 need DC. You don't have a rectifier. Hence, this doesn't work.

Build a rectifier.

If you build a 3-phase rectifier, you will leed relatively little capacitance to stabilized the output voltage. How much you'll really need depends on your requirements for voltage accuracy, and the current you draw and the current the generator can supply.

PS: You're operating the 7805 outside its specification by providing it an inverted supply voltage half of the time; that's why it shuts down. Chances are that doing that damages the IC.