Yes. Strawberries do well in pots.

I think my strawberries did even better in pots than they are doing in the ground. Just keep them watered every day or two -- they like it wet.

Agreed.

I have moved strawberries numerous times in a single season before without much problem. If you can get all/most of the roots, you shouldn't have any problem at all.

They might look really weak (droopy and browned leaves)for a few days, but should bounce back quickly.

After transplanting, you might want to leave the pot in a less shady, but not full sun location for a few days before moving it into full sun, assuming that's where you will ultimately put it. Suddenly moving them from shade to full sun could stress them out, and the combo of transplant and sudden increase in sun could be unnecessarily problematic. Transplant now, then gradually move them into full sun in a week or so if you want to be extra careful.

Also, once established, most (maybe all) varieties will spread like crazy, so you may want to consider that when determining pot size and number of plants per pot.

Thank you all so much my other question is what kind of soil should I put in the pot

You are definitely right to move them to a spot with more sun. I planted around a dozen plants in the spring of 2011. The next 2 years I got no berries at all (aside from the few which animals ate), as there were large trees along the property line which limited them to ~4 hours sun. This spring, I got most of the trees removed (which cost $$) and it has made a huge difference (8+ hours of sun). This year I got 20+ quarts.

One thing to note- even in a sun-deprived location, they still spread like crazy. The dozen plants spread to cover ~250 square feet, even before I removed the trees.

In terms of potting soil, you can make your own 5-1-1 (as described in the container forum) out of pine bark (5 parts), perlite (1 part), and peat moss (1 part). But, if you just want a little, it is probably easier to buy a bag of potting mix from HD.

As LawAndDisorder said, make sure they get shade and plenty of water for the first week or two after transplanting. Mine spread so well that I've potted some up and givent hem to friends and it works pretty well. You won't get a ton of production out of the small pots (quart or 4"), but it would work fine as a temporary home, if you wanted to later re-plant in a sunnier spot.