Interesting thing about how pugs in the "west" have been bred. Some friends rescued a couple from China (where the breed originated). Nowhere near as short/snub nosed as the western breed.

At any rate, if you have time, take the dogs by surface to the U.K. if you can (presents its own set of challenges) and then take them on a Cunard ship to the U.S. (might be able to take the Cunard ship from other European countries to the U.S. Then continue by surface to OK (it ain't gonna be Amtrak unless you pony up a private car at ~$4 a mile).

To answer your questions, dogs will normally travel on the same flight as you. Do allow plenty of time for layovers so the dogs make the connections. Look up what current US Customs/CBP and USDA regulations are for dog importation.

The fees for dog handling could be quite substantial. The cruise may not be much more expensive, if you can get the dogs to the U.K.