Oriental poppies do best when divided and transplanted in the fall. This is the traditional way. However, if you are waiting to claim the spot where they are now, I'd take a chance on moving them right away. Be sure to water them well the night before and have their new place ready. Take a good sized clump of soil with them to disturb the fleshy roots as little as possible.
After planting, they will lose their leaves and become dormant as usual, so don't worry about that. If you are just going to plant annuals in their place, you can plant these over the top of the poppies with little disturbance, and then move the poppies in the fall.