The wattage of the amplifier is under ideal conditions, I can tell you right now your conditions are most likely not ideal as they rarely ever are. The LM386 has a max output of 0.5W and it is impossible to exceed that limit for any number of reasons. The main reason is that if you try to exceed that you
will destroy the amp. The output power is defined by the input power, the gain and the supply power. It sounds like you are trying to gain power out of the amp that isn't there.
The capicitor and resistor in series connected to the output are for stabalising the amplifier. Without them the IC will oscillate wildly and it will sound horible. The large capacitor in series with the speaker is a decoupling capacitor, also known as a DC blocking capacitor in some aplications. It is there so that the output of the amp is not shorted when the speaker is connected. Try to bypass this cappacitor and you will destroy your IC.
The maximum current coming out of most amplifiers is realatively small unless it is specified as a power amp. You can find out how much current you can get out of an amp if you look up it's data sheet. A good place to get data sheets is
http://datasheetcatalog.com/
The max output power of an LM386N-4 with a supply voltage of 16V and a load of 32 ohms, the power can be between 750mW (0.75W) to 1000mW (1W). Trying to aim for a higher current is probably useless and I would not even try.
As for the LM384 the max output is 5.5W with an 8 ohm load, but it doesn't specify a supply voltage for that power output so I'm assuming that it is 28V. The max ouput current is 1.3A when shorted, shorted is the key word here.
It would help us more if we knew specificaly what you were trying to do with your circuit.