All human beings are ultimately of the same stock and there has been plenty of genetic mixing over the years. There is a reason why there is a northern band of Ural-Altaic languages running from Finland to Japan and a southern band of Indo-European languages running from Ireland and Iceland to India and China. In some cases, the Europeans went East. In other cases, the Asians went West. Look at the Lapps in Finland or the Europeans that carried Tocharian to China. And there was also quite a bit of North to South churning, too (there is a reason why there are dark haired and dark skinned Irishmen and I've read that the Japanese have a Malaysian genetic component as well as a Siberian one).
If you are really interested in the topic, I'd suggest doing a search on Amazon for Luigi Luca Cavalli-Sforza and take a look at his History and Geography of Human Genes. I also personally suspect (and some initial studies in Europe seem to suggest this) that they will ultimately find a different pattern of X and Y chromosome inheritence in many areas due to foreign warriors marrying local women and women being sent to other groups in trade.
Finally, I'd warn against confusing genetics and languages or cultures. "German" and "Celtic" are language and culture based divisions, not necessarily genetic divisions. Remember that the "Celts" once spread from Greece to Ireland yet the "Celts" on the fringes of Ireland and Scotland are genetically simliar to the Basques of Spain while I suspect the "Celts" in Macedonia were genetically closer to the Greeks or Hittites. Why? Just because a language or culture moves does not mean that genetics are carrying it. And even where the genes do move with the language and culture, there was (and still is) plenty of mixing and assimilation rather than replacement or extermination.
To put this another way, the people of Ireland and Scotland are not now genetically Germanic or Italic simply because they now speek a Germanic pidgin language with Italic influences (English). African-Americans do not magically gain Germanic genes simply because they speak English, either, or have picked up European religions or cultural elements. Genes do not carry language and culture nor do language and culture follow neat genetic boundaries. Yes, there are African-Americans with Northern European genes because of the now close contact between those two genetic pools in the United States and elsewhere. There are also plenty of European Americans walking around with American Indian, Asian, and African genes for much the same reason. A similar process has been going on for thousands, if not millions, of years. Even in the case of the widespread replacement and extermination of the indiginous people in North America, there are plenty of American Indian genes in the European gene pool and plenty of European genes in the American Indian gene pool.