As I understand it, there are two distinctly different "dark" things out there. One is dark matter. Clumps of material (usually called baryonic matter) which we can't see like burned out stars, gas clouds, neutrino's, MACHO's, and black holes (though the holes are not necessarily "matter" any more).
The other dark thing (the more interesting one) is dark energy. There appears to be an "essence" to the universe which we do not understand yet, which causes the acceleration of the universe and adds to its overall mass.
The ratio of parts is fairly well agreed upon at this point: 73 percent dark energy, 23 percent cold dark matter, and only 4 percent atoms.
Strings are predictions of a mathematical model which attempts to combine QED with GR. Because they are proposed as the structural element of EVERYTHING, even energy, they would not be thought of as a "piece" of the puzzle when it comes to identifying the missing mass in the Universe, because everything is made up of strings, dark matter as well as dark energy and any other dark thing we can think of.