Ok here's the deal on Overdrive, distortion, compressor
Overdrive - It's called overdrive because it was first produced without pedals on tube amps. It is made by driving and amplifier more than it can handle. I.e. The signal is too high for the speaker, therefore the sound becomes a little distorted. This is called overdrive.
Compressor - It is basically a device that makes your guitar tones evenly balanced. i.e. When you play soft it raises the signal and when you play loud, it lowers the signal. Therefore, all notes sound almost the same. This also allows for longer sustain because of the compression.
Distortion - Think of each signal as a wave made up of 3 parts. Bass, Mids and Trebles. Distortion cuts off the extreme highs and lows. In other words, it eliminates the highest highs and lowest lows, leaving only the mids and a funny signal, therefore creating a distortion effect.
Feel free to PM me if you want any more answers on these efx or even other efx.
A compressor balances the volume of the signal, not necessarily the strings (though often, then thicker strings are louder). What happens is that when you pluck a not, the sound has a certain amplitude (volume) and this can vary as you play across the strings and as a result of the different strings, pole piece heights, etc... What the compressor does is to make louder noises quieter and softer noises louder so that all sounds end up being roughly the same volume. This smoothes out the sound.
An overdrive is a completely different thing. This effect is meant to simulate the sound of an 'overdriven' tube (valve) amp circuit. What this means, roughly speaking, is that the tubes are pushed beyond their normal tolerances, which results in distortion of the sound wave. Depending on the components, this can result in a pleasing warmer, thicker sound for each note, with rich harmonic content. I'm sure some of the amp gurus on this forum can supply exact details about waves and amplitudes and scientific stuff, but all you need to know know is that an overdrive will thicken up and 'dirty' the guitar sound.
An EQ pedal is basically an elaborate tone control.
Normally, you see EQ pedals or rack units with a number of different sliders (regular ones) or tone pots (parametric). I'll describe regular ones.
Take a 5 band eq for example with 5 sliders that would be roughly Bass, Bass-middle, Middle, Middle Treble, Treble (normally you see a reading in Hz which measures frequency) so you can see the sounds are affected from lower to higher. You can get very fine resolution ones with dozens of thinner frequency band sliders, or you can rely purely on the tone controls on your amp. The three pots (Bass, Middle, Treble) form a 3 band EQ.
Moving the sliders up and down raises or lowers the volume of the different bands by a degree of decibels. That's it. It's used to sculpt the sound output. If you have an annoying trebly cutting guitar, then lower the high frequency range sliders. If your sound doesn't have enough 'oomph' then raise the low frequency range. Experiment. Useful to have, though not absolutely necessary. I have a Boss GE-7. It's adequate.