Hi Akramer,
What kind of LED are they? I only ask because if they are infrared, they have an extremely high current consumption over standard red, blue, green, white LED's. Just keep in mind that a 9v rechargable, is not 9v, but 8.4v. (AA, AAA, C and D are 1.2v not 1.5). Another important thing to understand is that standard LED's have a 0.7v forward voltage drop across them, so the voltage will drop by 0.7 when they are on.
Assuming they are normal colour LED's there is a couple of ways to wire them up.
The easiest way would be to could run multiple LED's in series (daisy chained), then put those multiple series circuits in parallel with each other.
Each series circuit you would run 3 x LED's in series along with a resistor. To calculate the resistor needed use the formula "R = Vs - Vfd / I".
R = Is the resistor needed.
Vs = Is the Voltage source, in your case 8.4v.
Vfd = I is the foward voltage drop of the LED(s).
I = Is the current (amps) the LEDs will draw (being in this case your LED's would be in series, you add the [u]voltage [/u]together to get the total, [u]not[/u] the current).
So appling that would look like
R = Vs - Vfd / I
R = 8.4v - (3 * 0.7v) / 0.020
R = 8.4 - 2.1 / 0.020
R = 6.3 / 0.020
R = 315 ohms.
A 315 ohm resistor does not exist in the standard 48 range of resistors, but you can just go to the next highest, 330 ohms.
Make 6 sets of those, and put them all in parallel, and you have your 18 LED's awaiting your rechargable battery.
I am out of time for now, Ill try to get back soon to help with the solar panel charging, unless pepe gets in first

Hope this helps,
Josh