What is this opening system for black?

In the general forums several players said that black can respond to any white opening with the moves ...d6 ...c6 and ...Nf6. What opening system is this for black? Where can I learn more about it?

All the three at once is certainly a bad idea.

1...Nf6 leads to completely different games depending on White's first move - there is a group of Indian defenses after 1.d4/1.c4/1.Nf3 1...Nf6, where you have to navigate through the transpositions into various but similar systems, but 1.e4 Nf6 is the Alekhine defense which is totally different (usually it goes on 2.e5, but some years ago there was a fad of the 2.Bc4 Nxe5 3.Bxf7+ Kxf7 4.Qh5+ variant ; it can also transpose to quiet 1.e4 e5 lines with 2.Nc3 e5).

1...d6 followed usually by 2...Nf6, 3...g6 etc. is the Pirc/Modern. Playing ...c6 after that is not a good idea : you might want to play ...c7-c5 later instead, for instance.

1...c6 invites a Caro-Kahn after 1.e4 c6 2.d4 d5 or 1.d4 c6 2.e4 d5. However, White can choose a Slav after 1.d4 c6 2.c4 (refusing the 2.e4 transposition) where Black has not much better than 2...d5 anyways.

You can get some basic advice about openings in the forums here. As a premium member you probably have some videos too, and there are some comments in the game explorer opening moves if I remember correctly. If you want to go serious you need probably a book.

play logical moves and good tactics

Venturing ...d6...c6...Nf6 against anything is possible.  I recall DeepBlue-Kasparov 1997, Game 4.  If White puts up e4 d4 and c4 then you have a generic Indian defense.  The Pribyl Defense is 1 e4 d6 2 d4 Nf6 3 Nc3 c6 with ideas of ...Qa5.  Some folks with a sense of humor have experimented with computer programs on the following type of position where White is granted full development in the form of a fist:

In such positions, Black typically opts for ...d6 and ...c6 and the quirk of it all is, the computer programs often fail to win from the White side.

 It depends.  It is just an inferior way to respond to many White openings.

It is not really an opening system as the moves are bad if applied to ANY opening.

The system might transpose to a Pirc Defense if White opens 1.e4

 However the "system" does  not do so well against 1. c4  or 1. d4

thanks for the helpful thorough answer. 

Certainly, but it's not very good. (1...Nf6 2...Ng8 against anything is possible too)

Even when you manage more or less to transpose to ...e5 KID lines (which White should not allow), ...c7-c6 could have waited and White should with precise play be able to take advantage of it.

Now, of course it's playable up to a certain level. But as hard as I hate the Pirc, I must admit I let Black escape with an equal game most of the time, whereas no such thing happens when ...c6 is played. Maybe I met only weak players to play it though.

Against e4 you get a Czech defence. It's not bad and the only way White can get an advantage is by playing f4 against it. There are some nasty traps there. 

Against 1.d4 you can try 1...d6 2.c4 c6 3.Nc3 Nf6 4.e4 e5 and get an old  Indian. It's a bit passive and masters will really squeeze you. Against everyone else it's probably fine.