I've tried with several "audio signals": mic (old fixline-telephone), mp3 player, guitar jack, android-app sinewave generator... in some cases the signal is above 20mV, ok (measured with an entry level 50$ digital oscilloscope); but as soon as I couldn't succeed in amplify above x10 factor the output is rubbish for AnalogRead of an Arduino UNO.
There's several ways we can go about this.
1- You can tell us you have never done this before and have no idea what you are doing and they we can tell you the correct way and you can tell us all the reasons you didn't do it that way. (time consuming , basically non-productive, and some OP's are very defensive and overreact when told they don't have a clue)
FYI, how do we know you have never done this before ?
So far, whatever circuit I've tried (with OpAmp IC like LM386... with generic OpAmp circuit based on transistors and so on) I didn't manage to reach a gain greater than x10 or so! Such an output voltage is useless for AnalogRead.
As already pointed out, you are trying to use a saw as a hammer. The LM386 is an audio amplifier. It is not designed to amplify a signal for data acquisition. It is designed to amplify a signal for the human ear.
Secondly, it isn't even an op amp.
after struggling a lot with OpAmps with no satisfactory results
So we actually would have been quite surprised if you had succeeded using that chip.
2- You can post a schematic of ONE of the circuits you tried for ONE of the many different inputs , all of which require their own unique input circuit (there is no ONE SIZE FITS ALL low level input amp-That kind of amp requires two adjustable gain pots, one called COARSE, the other called FINE) and then we can systematically explain why THAT particular circuit won't work. (since you listed many different inputs, each of which would (SHOULD) have a DIFFERENT design, this won't help you much because you won't know why the OTHER circuits you tried didn't work.
3- You can pick ONE of the various inputs you listed and we can show you the proper design for THAT particular type of input. This involves discussing some of the more common mistakes made by people trying to do this with no electronics background.
a- An AC signal needs to be coupled with a capacitor
b- On the output of the cap, the signal needs to be biased at the midpoint to use the upper analog
range for the positive transition and the lower half of the range for the negative transistion of the
audio signal. A voltage divider of two resistors greater than 10k and less than 50k will work for
this. (10k is typical)
c- A low level signal, whether ac or dc cannot be amplified more than 50 times by a single stage.
I have used a Differential Amp to amplify a 20 mV signal to 1V using a single stage. (A =50)
Look at the Single Supply Instrumentation Amp on the first page of this datasheet.
(Look at the frequency response graph. Gain is 20 for Diff input. [(1+1020/113)+(1+1020/113)]
You would need probably two more stages to get the signal to +/- 2.2V (4.4 Vtotal)
You choose: 1, 2, or 3 ?