I (or my mother when she comes to visit from the US) often bring over seeds on international flights. The problem with the post, at least to central Europe, is that it can either be fast or terribly slow. I lost half of some kiwis I ordered from Slovakia's neighbor Czech Republic because the courier was too lazy to drive out to our village right away, so they were boxed for four or five days instead of two.
I have actually ordered once seeds internationally from the U.S., and I had no problem with that, as well the company selling the seeds said they often ship to EU countries without problem. But, seeds may be subject to different regulations than grown plants.
Also there is customs. I do not know the laws on importing of plants into the EU, but I suggest you check what EU regulations are. Whether customs intercepts a package is pretty hit-or-miss, but just make sure you aren't setting yourself up for some big fine if they do. I have looked up just now what seems to be the relevant regulation:
http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:2000L0029:20090303:EN:HTML
See Annex III, Part A:
PLANTS, PLANT PRODUCTS AND OTHER OBJECTS THE INTRODUCTION OF WHICH SHALL BE PROHIBITED IN ALL MEMBER STATES
Plants of Abies Mill., Cedrus Trew, Chamaecyparis Spach, Juniperus L., Larix Mill., Picea A. Dietr., Pinus L., Pseudotsuga Carr. and Tsuga Carr., other than fruit and seeds
Plants of Castanea Mill., and Quercus L., with leaves, other than fruit and seeds
Plants of Populus L., with leaves, other than fruit and seeds
I'm not a lawyer, but I'm guessing that "Plants of Castanea Mill., and Quercus L., with leaves, other than fruit and seeds" means that if the oak seedlings don't have any leaves on them, you can import them. There is no mention that particular directive of sunchokes at all, though normal sunflowers are mentioned.
However, ANNEX V lists all species of Quercus as requiring a phytosanitary certificate. Still nothing about the sunchokes.
So, I think you'd get away with the sunchokes if customs intercepts, but they'd probably destroy the oaks. What sort of fines (if any) there might be is probably up to national governments. If you're desperate to try to get the oaks, then at least remove all the leaves, since this is apparently where whatever diseases the EU is concerned about stays. If its a lot of oaks and a financially significant investment, you might check what is involved with getting a phytosanitary certificate in the U.S. valid for imports into the EU.