I ordered these and got them in the mail today. On the site I ordered them from, it says to soak in water immediately and plant within 24 hours of delivery. On a website I looked at, it says keep the roots damp until you can plant them but don't soak them. Which is correct? How to do take care of these before and after planting them?

I'd interpret your info as meaning that if you soak overnight, and plant within 24 hours, you should be fine. If you can't get your seedlings planted that quickly, soaking plants too long could lead to rot.

I'm not sure how you'd be expected to keep the roots of 100 seedlings damp without soaking, but I think the idea is to encourage you to get those puppies in the ground quickly.

Happy planting,
Virginia

I could keep them damp with wet paper towels. Would it be better to keep them damp until Saturday or soak them in water and plant them tomorrow?

Loblollys are weeds...
Doesn't make that much difference.
I'd keep cool, moisture is secondary.
They usually come with slurry on roots, don't want to wash that off.