An undefined reference means that you are not linking all that's required or linking objects/libraries in the wrong order.
In your case
jni/Game.cpp:14: error: undefined reference to 'sf::String::String(char const*, std::locale const&)'
This is found in sfml-system
jni/ResourceManager.cpp:69: error: undefined reference to 'sf::Texture::loadFromFile(std::string const&, sf::Rect<int> const&)'
sfml-graphics for this one
jni/ResourceManager.cpp:83: error: undefined reference to 'sf::Font::loadFromFile(std::string const&)'
This is also in sfml-graphics
jni/ResourceManager.cpp:108: error: undefined reference to 'sf::SoundBuffer::loadFromFile(std::string const&)'
This one can be found in sfml-audio
jni/ResourceManager.cpp:170: error: undefined reference to 'sf::Music::openFromFile(std::string const&)'
And the final one is also in sfml-audio
Your "LOCAL_SHARED_LIBRARIES" list seems to indicate that you do indeed link all of those libraries, so I'm guessing that it must be the link order that's wrong.
I don't really know the Android build system, so I don't know in what order libraries on that list end up actually being passed to the linker (but I would guess it's either in the listed order or reverse order).
The rule to remember is that libraries or object files needing a symbol need to be listed before libraries/objects satisfying the dependency. So If you have 3 objects A, B and C and B needs something from both A and C and additionally C needs something from A, you'd link them in the order: B C A
I think the link order only really matters with static libraries, but I'm not 100% certain and personally just always follow the little rule above.