Definately pot them up and keep them in a nursery area until Fall if you can keep them watered; that's the hard part, keeping them watered. Then plant out. Or plant in ground in a temporary area nersery bed which is much easier to keep watered. They wont dry out as much either in ground. Identifying them will be easier next year, according to leaf shape. Been there, doing that currently.

Why are they soaking in water????

I would plant them in small individual pots in a VERY well drained potting medium (not your garden soil). Keep them in an area where you can keep track of them, as small containers require frequent watering.

What about sunlight? Since I don't know what they are really or how much sun they require, what should I do? If I keep them on my back deck, it'll be easier to keep track of them and keep them watered, but I'm concerned because the sun is quite harsh there.

Put them in dappled shade or morning sun so that the pots won't dry out so quickly. I got some redbuds from the ADF two years ago that I babied in pots until fall. First they have to get some size until they were big enough to plant out and secondly you'll have to do a lot less watering planting out in the fall. I move things around at all times of the year, but woody plants are best moved in fall/winter.

Well, I potten them all up with all the largest pots I had. I need to get a few bigger pots to move some to. One was lost but I have 10 viable! Thanks all.

Something else to consider. Pot them up indvidually and then sink the pots into the ground. They'll grow better and be easier to take care of and will be eaiser to take up in fall and place in their new homes.