The Aryans aren't the same as all Indo-Europeans. They were a Bronze Age group from Iran which spread into central Asia and India. They and the Greco-Latins probably originated in the Black Sea basin which was filled in by the Mediterranean in about 5500 BC. I doubt Nordics were originally Indo-Europeans. Rather, they were Finns before becoming Indo-Europeans. Only as "Aryans" pushed west did the Celtic and Nordic languages form...
The Germanic people crossed into Scandinavia sometime between 1600 and 700BCE. At this time the Finnish people had not come into existence; the Uralic people living in that region at that time were the Sami (formerly called "Lapps")--who actually arrived about the same time as the Germanic people. Since they inhabited different parts of the region, it's reasonable to believe the DNA evidence and say that they were unrelated: the Germanic people were Indo-European and the Sami were Uralic.
The first Indo-European tribe to enter Europe was the Celts, and they pretty much had the place to themselves for several centuries. Coming from a region where the technology of agriculture had been established for millennia, they quickly dominated the still-Paleolithic Cro-Magnon and marginalized them. It's been suggested that the Basques are the only living descendants of the Cro-Magnon (since they are clearly not Indo-Europeans nor of any other known ethnic group), but since we apparently don't have any clean samples of Cro-Magnon DNA, we may never be able to answer that question.
Other non-Indo-European peoples found their way to Europe. The most well-known were the Etruscans. Again, we have no DNA samples; coupled with the fact that we have so few examples of their language that we can't decipher it, this makes it impossible to figure out where they came from.
The Hellenic and Italic tribes arrived in southeastern Europe about 3,000 years ago, and established a great civilization which, arguably, is the same one we live in now. (Speaking for the Americans and Europeans on this website.)
The Celts were so thoroughly overrun by the next wave of invaders that they have, in turn, been marginalized. Ireland, Scotland, Wales and Brittany are the only places where Celtic languages are spoken and the people have primarily Celtic ancestry. Cornwall and the Isle of Man are also populated by Celtic people, and there is a movement to restore their Celtic languages, which are well recorded.