QQ has Harry's wand, so how is Harry going to get out of this mess? One of my theories is wandlessmagic. The existence of wandless magic at all is evidence the wand isn't strictly needed.

This makes sense if you buy that a wizard is pulling levers on the source of magic rather than actually enacting the spell

From Chapter 25

If magic had been like that, a big complex adaptation with lots of necessary genes, then a wizard mating with a Muggle would have resulted in a child with only half those parts and half the machine wouldn't do much. And so there would have been no Muggleborns, ever. Even if all the pieces had individually gotten into the Muggle gene pool, they'd never reassemble all in one place to form a wizard.

...

So however your genes made you a wizard, it wasn't by containing the blueprints for complicated machinery. That was the other reason Harry had guessed the Mendelian pattern would be there. If magical genes weren't complicated, why would there be more than one?

And yet magic itself seemed pretty complicated. A door-locking spell would prevent the door from opening and prevent you from Transfiguring the hinges and resist Finite Incantatem and Alohomora. Many elements all pointing in the same direction: you could call that goal-orientation, or in simpler language, purposefulness.

There were only two known causes of purposeful complexity. Natural selection, which produced things like butterflies. And intelligent engineering, which produced things like cars.

Magic didn't seem like something that had self-replicated into existence. Spells were purposefully complicated, but not, like a butterfly, complicated for the purpose of making copies of themselves. Spells were complicated for the purpose of serving their user, like a car.

Some intelligent engineer, then, had created the Source of Magic, and told it to pay attention to a particular DNA marker.

...

The line of reasoning continued: Atlantis had been an isolated civilization that had somehow brought into being the Source of Magic, and told it to serve only people with the Atlantean genetic marker, the blood of Atlantis.

And by similar logic: The words a wizard spoke, the wand movements, those weren't complicated enough of themselves to build up the spell effects from scratch - not the way that the three billion base pairs of human DNA actually were complicated enough to build a human body from scratch, not the way that computer programs took up thousands of bytes of data.

So the words and wand movements were just triggers, levers pulled on some hidden and more complex machine. Buttons, not blueprints.

Since wandless magic exists, we know that you can push those buttons without a wand. You can make the source of magic do what you want without a wand. Harry has been told that wandless magic is harder or that it requires more power, or various other excuses for it not to be taught until later. But, I suspect that is just a conceptual limitation, that you don't actually need the power to do it. My evidence for this is the accidental magic that children use when stressed. Under stress children can perform magics that seem extremely powerful (well over the power level of kids their age) and they can do it without wands.

from chapter 13

Now Professor Sprout was giving Harry a sceptical look. "I suppose this boy hit himself with two pies, then." "He didn't use his wand!" blurted one of the young Hufflepuffs. "I don't know how he did it either, he just snapped his fingers and there was pie!" ... "Prior Incantato," said Sprout. She frowned. "That's odd, your wand doesn't seem to have been used at all." Harry shrugged. "It hasn't, actually, I only got my wand and schoolbooks a few days ago." Sprout nodded. "Then we have a clear case of accidental magic from a boy who felt threatened. And the rules plainly state that you are not to be held responsible.

Now in this case, we know that it wasn't accidental magic. But Sprout, a Hogwarts professor and presumably an expert in dealing with wizard children thinks this is perfectly plausible. She thinks Harry could create, not just transfigure, but create two pies ex nihilo and then levitate them at high speeds towards a bully. (brief aside consider the amount of energy in two pies)

in chapter78

Mr. and Mrs. Davis were shaking as they stood up from the comfortable chairs of the faculty Quidditch box; they couldn't quite clutch each other while walking, but they held hands tightly, pretending hard to be invisible. If they'd been children young enough for accidental magic they probably would've spontaneously Disillusioned themselves.

We've been told elsewhere that disillusioning is very high powered magic. After the dementor incident, QQ notes, that Snape is probably powerful enough to disillusion himself. From context, this is notable and its assumed that many adult wizards are not able to do it. But the above quote from 78 says that children CAN do this if they have the right frame of mind.

"Accidental" magic gives children a way to press the buttons on the source of magic without wands, incantations or movements, and it gives them a way to press the buttons for spells that are otherwise far above their power level. If Harry promotes this problem / subject to his attention, then he may discover a way to deliberately use "accidental" magic. And once he had that, he would have a vast toolkit at his disposal.