Amps, I've got figured out. 1 coulomb of electrons is 6.24*10^18 electrons. That many electrons moving past a point in one second is one amp. So I think I've got that one sorted. Similarly, Ohms is resistance... the more ohms, the more resistance, the fewer electrons make it through.
Let me see if I can try a different approach to what everyone else has used.
It's probably useful to introduce ohms law at this point:
E=I*R
So I is current or as you stated.. how many electrons which pass a given point.
R is resistance, or how difficult it is to push electrons around a circuit.
E is voltage. Or EMF... Electro-Motive-Force. Volts just happens to be the unit.
If you think of it this way:
Current is the actual movement of electrons.
Resistance is how hard it is to move the electrons.
Voltage is how much force is being applied to the electrons to move them.
Then things logically come out of this:
For a circuit with a given resistance, increasing the voltage will result in more electrons moving or more current, since there is more force being applied to the electrons to force them "through" the resistance.
For a circuit with a given voltage, reducing the resistance will increase the current since there is less opposition to the electrons moving. With the same amount of force being applied you logically will push more electrons.
Another way to think about this that just occured to me is if you think about pushing a car up a hill..... (or other rolling object),
Volts is how hard you push the car - think: more people and/or pushing harder would push the car faster.
Resistance is how much brake you apply - the harder you push the brake down the more difficult it is to push the car.
Current would be how far you move the car in a certain amount of time.
(and so you think about it when you get there: Watts is a combination of how hard you push the car and how far you move it - just multiply the two).
You could also think about this with a rock (the bigger rock the more resistance, how hard you push the rock is voltage, and how far the rock moves is current) or similar.
One other free resource that may be useful for you:
https://www.khanacademy.org/science/electrical-engineering (And I just looked and they use yet another way to try to describe voltage in an intuitive manner - it may work for you instead).