Has anyone used information theory to study the origin of life, and if so what were the findings?

There are a broad range of people who have written on the subject as well as far more who have written tangentially about the subject with significant knowledge in either the information theory or the microbiology camps, but not necessary great knowledge or experience in both. I maintain a large list of research papers, books, and journal articles on the free site Mendeley which you can browse here: http://www.mendeley.com/groups/2545131/itbio-information-theory-microbiology-evolution-and-complexity/. Not all papers directly address your question though several do, while in aggregate, they should go a long way toward answering your main question. While there has been some excellent groundwork in these areas, no one has come significantly close to giving a direct proof (and one may never exist, by the way) though there are some reasonable stabs in the direction of building some reasonable theory.  For a quick overview with some history and general results written for a broad audience, I'd recommend taking a look at Werner Loewenstein's book http://www.amazon.com/gp/product/B0014HBQAQ/ref=as_li_ss_tl?ie=UTF8&camp=1789&creative=390957&creativeASIN=B0014HBQAQ&linkCode=as2&tag=math01-20. In general, there are only about two dozen researchers in the world actively applying information theory to molecular biology while there are hundreds of others working at the fringes (usually without direct knowledge of the mathematics or even existence of information theory as a discipline of engineering), but it is an actively growing field, particularly in the past decade compared to the beginning efforts of researchers like Henry Quaestler and Hubert Yockey in the 60's whose work grew out of that by Shannon, Weiner, and von Neumann. For some interesting and early background on these areas and their philosophy, I'd also recommend taking a look at Claude Shannon's Ph.D. thesis from MIT (note: don't confuse this with his incredibly popular and influential Master's thesis) and Erwin Schrödinger's essay "What is Life?", both of which should be freely available on the web.

Yes, there is such a formalism, unique up to some silly details, described in this paper of mine: http://arxiv.org/abs/q-bio/0503028 .  It is a way of describing the interactions in a complex molecular system, from a computational point of view. The computational point of view is describing the information in the molecules, it's what you mean when you say "information theory", although the precise usage of the term in the literature is not quite what you are talking about. This research is the outgrowth of an origins-of-life hypothesis I described for the first time here: The main point for the origin of life is that all you need is a Turing complete molecular soup, and you're done. This solves the problem permanently and persuasively. The hypothesis is amenable to test by both simulation and experiment. The simulations simply simulate Turing complete automata, like Wolfram's, except in 3d, and with a bulk computing capacity (so potentially infinite strings at each cell with rewrite rules according to nearest neighbor or power-law decaying inteactions, modeling proteins). As Wolfram noted, every such system is Turing complete, unless it is random or trivial. The experimental test is simply to make an amino acid and petroleum/water mix under conditions where polypeptides spontaneously form. The system should, under certain conditions of salinity and Ph, form a computing system, and the result will then start evolving immediately, as described in the linked answer. This idea is original, so there are no references, other than the ones I linked here.