#2
They are different degrees of distortion. From weakest to strongest it would go gain, drive, overdrive, and distortion. Don't quote me on it, but I'm pretty sure.
#3
drive's another word for overdrive, so is distortion, and gain is the knob you turn to achieve it. the gain knob is actually a volume knob for the preamp, and the more you crank it, the more current passes through the tubes, making them overdriving or distorting and giving you that sound.
#4
Gain is a colloquial term. It has applications in electrical engineering, but the way guitarists use it, it basically means the amount of distortion. Drive refers to the same thing.

Overdrive occurs when an amplifying device is pushed past its limits. Those devices (tubes or transistors) respond to this by starting to clip the top of the waveform, which is what causes that blurry sound.
Distortion is much the same as overdrive, except that the waveform is severely clipped, so there is a definite affectation to the sound.

Overdrive is specifically using added volume to cause the change. Distortion does not necessarily involve adding volume. Overdrive is distortion, but a more specific and often less extreme type.

As darkflame said, it's all pretty much the same thing. It's not like there's a formal guitarist's definition for these things, so most of these terms end up meaning largely the same thing. Think about how broad the term "distortion" is - all it really means is that the original sound is altered - hence, distorted.