7 Motors and a Load sensor... current overload

Hey everyone,

HARDWARE: I'm working on a robotics project that requires 7 motors (3 servos and 4 regular DC motors). It also communicates with a load sensor (Serial I/O works just fine). I'll probably also need a few more motors at some point (up to 12). I am NOT using a motor shield, or any other type of shield.

SET UP: I am using two breadboards at the moment, with power/ground running parallel across all 7 motors, directly into the Mega's 5V output and GND. I'm using motor controllers (Vex) on the 2 wire motors to control them via the Mega's PWM pins, and the 3 wire motors are controlled the same way (minus the motor controllers).

ISSUE: I've been having trouble with the motors (inconsistency, low squealing, no rotation at all even with no load) and didn't realize it was the current until days later. That had not been on my mind at all, as I've been learning as I go. All of my motors (and the rest of my parts [minus the load sensor]) are Vex. If it makes any difference to the current it draws (which wouldn't make sense to me), Arduino treats the regular DC motors as servos as well.

ATTEMPT AT SOLUTION: I made a makeshift battery holder (9V, 6 AA's) and tried powering the Arduino with that instead of by USB. Needless to say, that was a stupid, desperate thing to try... was just hoping it would supply that little extra. I also tried to connect all of the motors directly to that battery (in parallel), with the Mega connected to my computer, powering itself separately. The motors began spazzing out (including motors that should not have been moving with the code that was uploaded), so I'm absolutely lost.

I've been searching the forum but having trouble finding a similar scenario that I understand. I'll continue searching and adding additional information to this thread, but I'm looking for some advice in the mean time.

Does anyone have any thoughts? I've seen a few posts about the H-bridge thing but I don't understand the purpose of it and I'm not sure it would help me. I'm absolutely able to go buy any components I need, or a real external power source if it will make my life easier.

TL;DR:
Board - Arduino Mega
3 Servo Motors (Vex) - http://www.vexrobotics.com/276-2162.html
4 DC Motors (Vex) - http://www.vexrobotics.com/276-2177.html
Load sensor - (Has it's own power source so I'm not too worried about that at this moment)

How to supply enough power/current?

Thanks to everyone.

EDIT:
PS: I've been trying to find a servo with 1080 (+ or -) degrees of rotation. Anyone know how to go about looking for something like that or perhaps how to make one?

Found this webpage on motors: Motors 1

Looks like I might need transistors to make this work. Sadly, I know absolutely nothing about transistors or diodes, despite finishing up my sophomore year of electrical engineering this spring.

Same guy posted this about power supplies: Power Supplies

My particular motors seem to do well between 5.5-9V so I think I'm going to pick up an 8V supply if I can find one. Gotta figure out current ratings...

This link talks about transistors and how they work with arduino + motors.

A different webpage said that transistors shouldn't be used for currents greater than 1A, but the motors I'm using have a stall current of 4.8A. Does that mean I should be using some sort of relay instead?

Apparently the transistors need diodes or something as well to keep them from getting destroyed by surges?

EDIT: http://www.instructables.com/id/Use-Arduino-with-TIP120-transistor-to-control-moto/
This link explains what everything does, and recommends which components to buy.

I think I've answered my own question at this point, but hopefully it helps someone else!