This is indeed a difficult question. If we say that a physical object is an object with intrinsic physical properties, then you are right: we have left ourselves with the question of what a physical property is. If we say that a physical object is an object with spatiotemporal properties (such as position and velocity), then someone who believed in irreducible minds or souls that have spatial locations could presumably still count as a physicalist, which seems inappropriate. If we say that a material object is an object that is made of matter, then we need an account of what matter is. Are electric fields made of matter? They have mass, after all. Would Newtonian space be made of matter? It doesn't seem like it would be ... but its existence does not compromise materialism, does it?
More generally, materialism and physicalism seem to be motivated by the idea that the entities described by physics are all of the entities that there are -- or, more precisely, are all of the fundamental entities there are. Another way to put this idea (that avoids the presupposition that there are fundamental entities) is that physicalism is the idea that all of the facts (or, at least, all of the contingent facts) are determined by the physical facts. Now, of course, the question is: what is a physical fact? Any specification of the particular kinds of properties that can figure in a physical fact would seem to be hostage to the fortunes of a future physics. To avoid any commitment to the kinds of facts that might appear in a final physics, we could say that physicalism is the idea that all of the (contingent) facts are determined by the facts that would appear in the final, complete physics. However, that way of putting the point presupposes that we understand what counts as "physics." This seems to raise exactly the questions that we were trying to get around.
One place where these matters are discussed is early in Bas Van Fraassen's book "The empirical stance." Van Fraassen argues that materialism (physicalism, naturalism...) are stances rather than views that could be true or false.
Why not? We can conceive a nice large space filled with moving matter, all as in our universe, except that the laws of nature vary randomly in space and time -- which is really to say that there are no laws of nature. You could still use geometry to describe the trajectories of objects, but you could not simplify these descriptions with general formulas that cover, say, the force that objects exert on one another. Nor of course could you project any descriptions into the future (predict what will happen) nor even describe with any accuracy what is happening elsewhere or what was happening in the past (because you would have no firm ground for reasoning backward from the data you have to their origins).
So it seems that we can conceive such a world. But whether a cognitive subject could have experience of such a world, could hold it together in one mind, that's another question, one that is very interestingly examined in Kant's Critique of Pure Reason.
Let's start with a quick comment about string theory. My knowledge is only journalistic, but it's clear that string theory is a mathematical theory and states its hypotheses about extra dimensions using mathematics. And as your comment about additional variables already suggests, there's nothing mathematically esoteric about higher dimensions. When variables have the right sort of independence, they represent distinct mathematical dimensions in a mathematical space, though not necessarily a physical space. (Quantum theory uses abstract spaces called Hilbert spaces that can have infinitely many dimensions. But these mathematical spaces don't represent space as we usually think of it.)
Of course, it might be that getting the right physics will call for the development of new branches of math. Remember, for example, that Newtonian physics called for the invention of Calculus, and though earlier thinkers had insights that helped pave the way, Calculus was something new. Just what sort of new mathematical ideas science might lead to is something we'll have to wait to see. But you've raised another question: if sound physics calls for new math, would the math we have now "still hold true" as you put it?
An example might help. General relativity tells us that the geometry of space-time isn't Euclid's geometry. It's something more complicated called pseudo-Reimannian geometry. Does that mean that Euclidean geometry isn't true?
A good answer calls for making a distinction. As a mathematical construction, there's nothing wrong with Euclidean geometry and there are lots of true statements that go with it. From the axioms of Euclidean geometry, it follows that the square of the hypotenuse of a right triangle is the sum of the squares of the other two sides. Briefly, it's true that Euclidean triangles satisfy Pythagoras's rule. However, this is a statement within math itself, so to speak. Whether physical space fits Euclid's axioms isn't a mathematical question but an empirical one, and the answer turns out to be "No" (or at least "not always.")
Here's a way to look at it: math gives us ways of describing possible structures. (Euclid's axioms describe a very general sort of possible structure.) We can construct abstract proofs about those structures whether or not they fit anything in physics. A theory in science might say that one kind of structure rather than another (this geometry rather than that, this probability distribution rather than that, this kind of differential equation rather than that...) gives us the best model of some part of physical reality. But changing our mind about which mathematical structures are good models for the world doesn't amount to changing our minds about math itself.
It's certainly true that Bohr and Heisenberg, among others, interpreted quantum theory in a way that put the knowing subject center stage, but this is just one part of a controversy that continues to this day. Einstein and Schrödinger, for rather different reasons, resisted these more epistemic interpretations, and while some would say that Einstein lost in the wake of the investigations of Bell's inequality, Bell himself was very attracted to realist interpretations of quantum theory. "Collapse" interpretations, such as the so-called GRW theory, are not epistemological interpretations, nor is Bohmian mechanics (a development of de Broglie's pilot wave idea), nor, for that matter, is the Everett interpretation (roughly, the "many-worlds" interpretation.)
So the simplest thing to say is that there partisans on both sides and the controversy is ongoing. If you'd like to read more, you could do worse than to get a copy of Alistair Rae's Quantum Physics: Illusion or Reality? or John Polkinghorne's Quantum Mechanics: A Very Short Introduction. Both of these books, written by physicists, cover the physical ideas and the interpretive approaches in a reasonably accessible way.
Here's an argument that the early modern philosophy Gottfried Wilhelm Leibniz gives for postulating the existence of an entity without parts, versions of which he gave from the 'middle' of his philosophical career--roughly, from about the time that he wrote the "Discourse on Metaphysics"--until the end, which, for present purposes, we can take to be the Monadology.
Leibniz starts from the fact that material things can all be subdivided--he actually says that material things not only can be divided, but that they are actually infinitely divided. Since a material thing such as a table can be, as it were, decomposed into infinite material parts, Leibniz argues--in a line of reasoning that is especially emphasized in his correspondence with the philosopher Antoine Arnauld based on issues in the "Discourse on Metaphysics," but elsewhere in his writings as well--that a material thing like a table is no more metaphysically real than a heap of stones, a flock of sheep, or a rainbow: the basis for this claim is Leibniz's view no TRUE ENTITY can be divisible. Consequently, Leibniz argues, if there are true entities, then they must be simple, immaterial things, that is, something like the monads, which have no parts and which, in Leibniz's ultimate formulation of his metaphysics in the Monadology ground the existence of all other things, and which, Leibniz concludes, not only exist, but are the only really existing things. (I leave aside the wrinkle that Leibniz also claims that material things are merely 'well-founded phenomena' phenomenally based, as it were, on the monads, not even things at all, a point closely related to his view that the only true entities are simple substances, but not directly following from it.)
Now, to be sure, Leibniz's position turns on his view that a true entity must be indivisible. Leibniz worries this point a great deal--for a masterful account of the ways in which he worries this point, I cannot recommend too highly R. C. Sleigh, Jr., Leibniz and Arnauld: A Commentary on Their Correspondence, which focuses on the correspondence, and Donald Rutherford, Leibniz and the Rational Order of Nature, which examines the topic more broadly across Leibniz's philosophical career.
The general issue about the relation between material parts and things is treated by numerous other early modern philosophers: Tom Holden undertakes a wonderful, searching examination of this topic in The Architecture of Matter: Galileo to Kant.
To follow up on my earlier response: In the February 10, 2011 edition of the New York Review of Books, Steven Weinberg has an excellent review of Hawking and Mlodinow's book. The review, which is also published online at URL http://www.nybooks.com/articles/archives/2011/feb/10/universes-we-still-dont-know , addresses some aspects of your question -- and also contains some good information about the theories that Hawking and Mlodinow are attempting to popularize.
A telescope collects more light than an ordinary human eye. It is a larger "light bucket". Consequently, a telescope helps us to see things that are fainter (as seen from earth) than we can with the naked eye. Consequently, a telescope helps us to see things that are more distant (and hence helps us to see things as they were longer ago). A terrestrial telescope does not "meet" light somewhere along the way, unfortunately. The light must still manage to arrive at Earth.
The obvious response is that there isn't a single response, and for a simple reason: quantum theory doesn't have anything to say (or not obviously, anyway) about souls -- at least not if a soul is some non-material thing that doesn't fit into the equations we use to do physics.
There is a view that's rather like many worlds and that allows for something soul-like. It's called the Many Minds interpretation, and you can read a short account of it (and get further references) by following this link:
However, this won't address your worries about the afterlife. And since this is a topic that physics has even less to say about than it says about souls, it's even clearer that there's no good answer.
That said, a handful of extra thoughts. The first is that IF there is a non-physical soul (a very big "if), then we can start by asking what happens to it after death on our usual non-quantum picture. And then we could say that whatever the story may be within a single world it's the story we should tell within branches of the Everettian multiverse. Whether that would call for a separate Heavens for each branch, or, if not, what God does about all the near-duplicate souls is a question far above my pay grade. Or possibly the soul doesn't divide but follows some one path through the garden, though which path and why that one rather than another is liable to remain a Great Mystery.
But what I'd really like to suggest is this: the idea of a detachable, non-physical soul is so nebulous as to be a dubious notion from any points of view. The main reason, near as I can tell, that many people believe in it is that they believe in an afterlife and think that the two ideas go hand in hand. In fact, they needn't. There are possible theories of an afterlife that aren't based on souls, and there are possible views of souls on which they don't survive eternally anyway. If talk of the soul is nothing more than a blank space to write a belief in the afterlife onto, then one might as well reason directly about the afterlife and associated issues about what it would mean for some being around after your death to be you. Saying "it's me if it has the same soul" is a case of trying to explain the obscure by the obscurer. If we add many-worlds quantum mechanics to that already unholy brew, the safest thing to say is that we have a recipe for intellectual indigestion.
Well, I cannot speak for all philosophers. But it seems to me that Hawking has not kept up with the developments in philosophy. Of course, he need not do so ... unless he plans to say something about them, as he apparently did.
There is a tremendous amount of very scientifically informed philosophy of science. People in philosophy departments and people in physics departments both work on the conceptual, logical, and metaphysical foundations of physics (and analogous points could be made about evolutionary biology or economics, for instance). Even a cursory glance at the literature would bear this out.
I apologize if this sounds somewhat defensive. I guess it is. But physicists do tend to deprecate philosophy of science without having taken the trouble to familiarize themselves with it. See, for instance, Steven Weinberg's book "Dreams of a Final Theory" (1992), to which Wesley Salmon replies in "Dreams of a Famous Physicist", an article reprinted in his book "Causality and Explanation".