Arduino Uno R3 with a high power servo PROBLEMS

Hi, Im an electrical engineering student working on a gyro stabilizing platform and I am using two HS-805BB+ MEGA 1/4 SCALE SERVOs with an Arduino Uno Rev3 board. Just using the standard Servo library and running the sweep example, my servo does not even work when its attached to 5V of the board, I have tried running both the board and servo off of a usb port, board off of wall outlet 9V dc and servo out of board/external 5V supply and to no avail. HOWEVER, for all these scenarios if I attach the servo voltage to 3.3V the servo actually runs the sweep code but is a bit jittery as the Servo data sheet suggest a 4.8-6.0V supply and has a 700mA no load running. I realize I will have to use an external supply for the servo (Eventually going to use two servos for my project), but why is my servo acting weird (also have tried with other servos identical and also a different one). My technical advisor suggests to use the Mega as he has had problems with the Uno aswell, but I just wanna know why. Also to note, when the servo is plugged in to the 5V it starts making ticking sounds and when everything is powered off of the usb my computer makes the sound when you unplug devices from a usb port.

but I just wanna know why.

Because your power supply setup for the servo power is BAD! It is surprising your pc USB port over current fuse hasn't tripped. Get an appropriate ~6v external power supply for the servos.

Thank you for the reply! But unfortunately I have tried that, (but to +5V and to a common ground, although it shouldn't make a difference since its rated for 4.8-6V). But, even if both were powered by the usb port, why would the 3.3V port cause the servo to move and not the 5V port? I was reading the Arduino servo library and I found that "The Servo library supports up to 12 motors on most Arduino boards and 48 on the Arduino Mega. On boards other than the Mega, use of the library disables analogWrite() (PWM) functionality on pins 9 and 10, whether or not there is a Servo on those pins. On the Mega, up to 12 servos can be used without interfering with PWM functionality; use of 12 to 23 motors will disable PWM on pins 11 and 12. " Also, if I power the board from the Vin pin to 9V and I have the usb connected to the board and my computer, in order to view the serial monitor, does the board get powered by default the Vin or the usb port, or does it depend on what it is driving? I hope my problems will be solved when the Mega 2560 comes in.

But unfortunately I have tried that, (but to +5V and to a common ground, although it shouldn't make a difference since its rated for 4.8-6V).

If the +5v is the arduino +5v, it will probably never work well.

I have tried the Arduino supplied with +9V (Vin pin) and the servo to +5V from an external supply and still it did the same thing. But it still bothers me that with everything powered by the usb port, why the servo would move for 3.3V and not 5V even if it doesn't have enough current to make the servo work properly. Cause for both cases it should not work if the supply isn't powerful enough.

Measure the current drawn by the servo.
Check to see the wall wart can deliver that current.

I can't tell you why the servo tries to run at 3 volts, but i'm sure it's not a good idea to even try it that way.
As sketched by zoomkat, always connect the grounds together.

The question about what power will be used in case USB is in use as well as an external power supply has been answered many times already.