In the Harry Potter universe, spells such as wingardium leviosa can move objects with no apparantly visible force being applied. Is there an canon explanation (or non canon otherwise) explanation of where this force comes from and how it isn't in violation of physical laws as we know them?
No, there is not any such explanation.
In fantasy fiction, there are basically two techniques for introducing magic into your story, which I will refer to as the "Tolkien method" and the "Sanderson method". I made those names up just now, but they are good representations of the very different methods of adding magic to a fantasy world.
For a really good explanation of Sanderson's style, you can read his "Laws of Magic", starting the article law #1, where he starts out by making the following claim: Magic must have rules. In a work that follows Sanderson's logic, you would expect to find some explanation for where magic comes from, how it works, why it works, etc. This is something that people like Sanderson, and Robert Jordan, are very well known for doing.
However, most high fantasy doesn't work that way. Instead, magic is left explicitly unexplained, because the author usually feels that explaining away magic ruins the magic. Note, for example, the reaction from the panel in that link to Sanderson's blog when he suggested that magic should have rules:
And every other person on the panel disagreed with me violently. “If you have lots of rules and boundaries for your magic,” they explained, “then you lose your sense of wonder! Fantasy is all about wonder! You can’t restrict yourself, or your imagination, by making your magic have rules!”
This is the way Mrs. Rowling approached magic in her books. She chose not to explain anything about magic, even if that meant that many aspects of it made no sense, or violated the laws of physics, or even were sometimes self-contradictory. It's magic, thus, there's no need or expectation for it to follow any coherent set of rules.
If that lack of explanation bothers you, you're not alone. There are a lot of people (including myself) that really strongly prefer the Sanderson-style of magic. But JKR's anything-goes made-up-as-you-go-along style is just as valid, and often makes for a more whimsical or enjoyable story (especially given HP's target audience).
So, in short: the force for levitating stuff in HP world comes from JKR's pen, and that's all there is to it.
I think that there is a very good canon explanation. The ability to use magic is native to very few people and seems to be defined by genetics - most of the kids in wizard families are capable of using magic. Also muggle born are actually far descendants of squibs.
Magic has its limits. For example we need the ministry with lots of people working there doing lots of stuff WITH MAGIC. If magic was limitless then there would have been just one wizard lazily flicking a wand and making things as they need to be.
Magic needs tools to be effective. Without a wand a wizard can cast only weak spells. Same like a musician can play something by just clapping some stones but it will sound much nicer if a piano is used.
In regard to the "laws of physics" - they are mathematical models proven to be true by experiments. We don't know whether they are universally true - we just haven't been able to prove them wrong for now.
So spells might look like they violate the laws of physics but it just because the definitions in these laws.
Well ... The book does not go into details HOW exactly does magic work but it's literature, not science article. Judging from the results the nature of magic will be very hard to research and formulate to a model.
If you want a real world example of a "wizard" - take a talented mathematician. He/she is capable of understanding concepts and solving problems that 99.99% (add more 9's here's) of the people will NEVER be able to understand no matter how hard they try. So they can freely be called muggles. If he/she is asked "how do you do it" then the answer would be "I just CAN".
Not that I recall. It's fantasy, so: magic's allowed. And doesn't need to be explained away (which it would have if HP was SF).