In my experience, tung oil can take up to a month to fully cure.

If you used pure tung oil, then it will likely take that long. Cutting it with orange oil can help a bit next time.

The only thing you can do now to speed it up is to keep it somewhere warm. However, it has probably cured enough that you could start using it now. Just give it another wipe down.

Hmmm, tung oil takes a while to set fully, but I've never had it be that "wet" after a week. Not enough to leave residue on touch.

Even if the plywood was treated in a way that made the finish not "stick", it shouldn't be leaving oil when touched, it should have just beaded up originally.

I'm not aware of anything that will speed it up though, not significantly. If you're already keeping the project in a relatively warm environment with good air flow, that's about as good as it gets. Like, this time of year, if it's outside, you might expect it to still be a little tacky to the touch, but not oily.

Honestly, I'm baffled why it would be giving up oil to touch at this point. I've never run into that, and it's my preferred finish for my canes and walking sticks, so I've used it a good bit since needing them. It's not a lot of usage, I only need the finish when I either get a new cane/stick, or one gets damaged enough to need refinishing, but I've built up a decent sized collection at this point. And it never happened with any of the takes furniture I've used it on.

Usually, it's dry to the touch in a few days at most. Never seen it take more than a week.

Hmm I wonder if your project has been stored in room temperature or was it outside in the cold?

I might use a solvent to wipe it down, with a light 220 grit sanding, then try again.

I’m also wondering if you might have skipped a step. You should apply the oil, wait 5 minutes or so, then wipe off the excess. Then keep it in room temperature for a day. Repeat three times and then buff or polish.