Glad to see enthusiasm. I'm sad to say you've been let down by the popular press. Here's the word from a real life particle physicist:
I would be very much happy and grateful to know if someone can explain me a little about the relation between Higgs Boson and Force of Gravitation(Gravitons if exists).
There is none. The Higgs field gives mass to some particles (but it does not cause most of the mass of you or me or any other everyday matter - that actually comes from the strong nuclear force). The Higgs boson is an excitation of the Higgs field and its discovery confirms that the simplest model of the Higgs field is (at least close to) correct. Even if it did cause all mass in nature, it still wouldn't be directly related to the gravitational force (for several reasons I won't go into here). Even massless particles feel gravity, as the famous deflection of light by the sun can attest! You can find good popular level discussion of the real physics of the Higgs at Prof. Matt Strassler's site.
By any means does Higgs Boson supports String Theory?
Nope. It doesn't contradict it either. In its current state string theory is neutral with respect to the standard model Higgs boson - there is no clear prediction one way or the other. String theory is probably compatible with a Higgs boson very much like the one we've seen, but it is also unnecessary for a description of the Higgs - the standard model was written down in the 70s well before string theory was the dominant paradigm in particle physics, and it is described perfectly well (so far!) by the standard model of particle physics.