Read audio from USB OTG
Well, finally, I found an app that can read music from an USB stick.

ES File Explorer

It is a file eplorer which: 

1) detects USB sticks

2) comes with a simple music player with basic functions

3) can create a playlist from a specified folder

4) can do this with USB folders 

While the player in itself is not exactly the most advanced one (it won't detect id3 tags on USB files, doesn't sort songs by Artist, Album or whatever else than alphabetical order) nor the most beautiful, it has all I need for listening music in the subway (which was my main goal here) i.e. making a playlist from my music folder and being able to shuffle it.

Hope it helps people who had the same problem as me.

Edit

This player has some problems. It crashes, don't detect the stick sometimes and often goes as far as restarting my phone. It does the job, but it does not do it well and the user experience is unpleasant. Therefore, if anybody has a better suggestion, please write an answer !