As others have stated, the 20A rating of your batteries is the ceiling (maximum) discharge current. Depending on who mfg'd your cells, that may be a peak rating or continuous. If you're using an APV (usually don't like less than 1.2-1.5 ohms) or mod that can handle it, you can get down to about .3-.5 ohms without destroying anything (generally).
Your battery can then theoretically discharge up to 20A max at any given time, and has a total capacity of 3100mAh - which means you can have it discharge 3.1A for one hour before it's discharged. Generally the capacity in mAh is the deciding factor that determines the physical size of a cell or battery, and the discharge rate is dependent upon the quality of the components and mfging. Also, just because a cell can discharge at 20A doesn't mean it's gonna throw 20A every time you hit the switch.
The easiest way to figure out how much power (watts) / current (amps) / voltage you're using is the power formula and Ohm's Law:
Power Formula: V x A = P
Where V is volts, A is amps, and P is watts.
Ohm's Law: V = A x R
Where V is volts, A is amps, and R is ohms. A simple way to visualize Ohm's Law is:
V
A R
Thus, you can multiply A and R to get V as above, or divide V by A to get R, or divide V by R to get A. This relationship predicts certain behaviors, such as:
If V is constant, any increase in R will decrease A.
If A is constant, any increase in R will increase V.
If R is constant, any increase in either A or V will also increase the other of A or V.
So, to use your battery, if your cell is at an operating V of 4.0 and you have installed a 0.5ohm coil, your battery will be sending 8A of current through it. If you use a 1ohm coil, it would be 4A, and so on. If you use a VW unit, you can calculate that at 10W, your cell will discharge between 2.381A and 2.778A with the cell V decreasing from 4.2V to 3.6V (which is the normal range for Li-Ion and LiPo cells). This sounds weird at first, but makes sense when you keep Ohm's Law in mind - as voltage decreases, amperage must increase proportionately in order to keep the overall power output at the same 10W level. If your wattage is fixed at 10W and you have a 0.5ohm coil, your amperage will be about 2.23A and your voltage about 4.48V.
Using these simple formulas and the technical specs for your wire, you can always determine what will be safe and what probably isn't.
Any other questions, post here or PM me and I'll be glad to help if I can.
Hope this helps,
Bill