Having done a quick search on Hutchinson, it seems the only physics myth he doesn't claim to have created is cold fusion. As far as I can tell, he has admitted himself to being unable to replicate any of his effects after 1991 - which seems a bit bizarre given that they would be worth a fortune if they were true. He should know the physics behind it, and if he could replicate even a small example under test conditions then he would quickly become one of the richest men in the world. So no, as he is selling 'video evidence' for $100 a throw rather than drinking cocktails in the carribean, I don't think there is much to those stories.
However, the claims to have worked with the military are likely to be true. Military research budgets (as far as I understand it) do have room for blue skies research and something wildly unlikely but potentially of enormous use can still be a good investment for them. If someone claims to be able to do something remarkable, like create anti-gravity, then I believe that would be something that would be researched. I believe that such a project was looked into in the UK as well. I am unaware of any positive results from this stuff, but then I am as outside that circle of research as anyone else and so can't really say. What I can say is that there is no physical effect that I know of that can produce anti-gravity.
Now to the second part of your question. If we understand gravity at the LHC, will we be able to do something useful with it, like create anti-gravity. First off, a few qualifiers. The Higgs boson is the physical manifestation of the Higgs field, a field that gives particles mass. How that mass is then affected by gravity is a separate question. This separate question deals with gravitons, and the unification of quantum mechanics with relativity - through string theory, M-theory, loop quantum gravity or some other speculative theory. We will not break that problem at the LHC unfortunately. We may get some further hints how to proceed, but we won't get the answer.
However, we believe that gravitons exist. All forces have a particle that carry the force. Electromagnetism has the photon, the weak nuclear force has the W and Z bosons, the strong nuclear force has the gluon. All these have been experimentally proven. The graviton has not. f we were to be able to study a graviton then we would get some insight into the theory of gravity at the quantum scale which would be truly amazing. The unification of relativity and quantum mechanics is the holy grail of particle physics and one that Einstein died trying to achieve.
So that's all great, but how does it apply to anti-gravity. Well, the problem is that gravity is an attractive force. There are no negative gravitational fielsds around. This is unlike electromagnetism in which you get positive and negative forces. Just try to push two like sign magnets together and you'll see. We currently have no structure that gives a negative gravitational force. You can also think of it this way. Gravity comes from the warping of space and time (yes, I know, but stay with me). Space-time can be thought of as a rubber sheet (really, the maths is surprisingly close). Drop a hevy weight on a rubber sheet and you get a dip. Now if you place a marble on that sheet, it rolls towards it. The problem is that we only know how to make depressions in the rubber sheet, we can't pull it up. If we could figure out that then we'd have a way of creating anti-gravity.
There is one light at the end of this tunnel (and in factone that might show up in the LHC tunnel). That's the existence of dark energy. Now I mentioned dark matter - an exotic matter that doesn't interact with light but makes up 5 times more of the universe than atoms and molecules - but dark energy is even more mysterious. Basically the universe is expanding and it keeps getting faster. Now the only force acting on the scale of galaxies and above is gravity and it's only attractive. So if gravity is the only game in town then everything should be getting closer together, or at least be slowing down as it expands. This is not the case. And the amount of energy needed to maintain this behaviour is huge. This repulsive force has been named dark enegy, and no-one really knows what it is. It may be some form of anti-gravity, but it could be hundreds of other things as well. Given this is a huge gap in our knowledge, we expect a major revolution in physics when it is understood. And revolutions in physics come with useful, or at least interesting, spin offs.
The first effect of any great discoveries will be new terms and ideas popping up in science fiction. Some of them will be wildly off, but others may be possible. Given some time and clever experimental physicists and engineers, we'll get new gadgets and tools from this stuff that we can't possibly predict now. However, it is a good bet that a revolution in our understanding of gravity will have an impact on everyday technologies. I just don't think we'll see that revolution at the LHC.
So back to the question. I don't think there's any top secret research being done at the LHC. I'm certain that there's no hidden understanding of what's going to be found at the LHC. To know what it was going to find, you'd have to have built one already - and it is far too large and expensive for any one country, or small group of countries, to build on its own - let alone a company or military research unit. Also, if it could be done on a smaller scale, we'd know about it. Governments don't spend this much money unless they know it really can't be done any other way. Finally, CERN is an entirely non-military institution. No military budget is funding the LHC, and all the research is public. It's one of the only areas of science where you can read any item of research without paying for a subscription. All research is out there and available to anyone. Just go to here uk.arxiv.org, click on the experimental high energy physics link and browse until your heart's content. It's nice to work in such an open field - and the reason why I think there are no great secret plans.
Oh, my papers are here if anyone is truly bored!