"Viking" religion seems to share a lot of interesting features with ancient Hinduism and Zoroastrianism. Of course, since they are all Indo-European, they should share a lot in common. But, some features seem to be uniquely Indo-Iranian except for the fact that they appear in Nordic cultures as well.
Some examples:
Controversially, the Nazi's believed that Germans were actually descended from "Aryans", or rather "Iranians". While I don't put any stock in their theories or methods, I am curious as to why the religions seem so similar in these specific ways. Especially since so many cultures that existed between northern Europe and India/Iran don't seem to share the same features.
I'm not sure I can adress everything in your questions, but I can probably address some of it.
First, Indra is a very complicated deity. He is a strongman and a warrior, yes, but also an important celestial and cosmogonic figure (for instance, he tears heaven from earth in the beginning). It's not at all obvious to me that Thor has more in common with Indra than Zeus and Heracles do.
As for the Asura-Deva-distinction, this is so different between Zoroastrianism and Vedic religion that it is difficult to draw any general rules at all. I don't know what you really see in common with the Aesir-Vanir distinction; certainly I don't see any obvious shared commonalities that don't exist with, say, the Titan-God distinction in Greek religion.
Tyr and Tishtrya share no etymological roots. Tyr is from Dieus Phtr, Father Sky, cognate with Zeus and Jupiter. Tishtrya is probably from a root referring to "the three stars" of Orion's Belt. "Tiri" seems to have actually been a separate god, at some point, but this isn't clear in the sources. Tishtrya has a bunch of different functions in different times and places, and is involved in a cosmic struggle similar to the one of Indra with Vrtra.
So is there any basis for direct interactions? I would say that the most likely source for diffusion (which the time frame certainly allows for) would be via Balto-Slavic groups, which have loanwords from Indo-Iranian languages, including "Bog" for God and "wayras" for "club" (The Vajra is the cudgel of Indra). The deity Perkunos is also pretty similar to Thor, which suggests that it's possible that there may have been some transmissions of tradition.
However, none of the examples you bring up are terribly strong, and the dissimilarity in some cases of Greek and Roman tradition, apart from being affected by our limited source material, can also be attributed to greater interaction with the Near East; Zeus shares many similarities with Canaanite storm deities, for example.
This isn't even getting into the thorny issue of how little we know of Norse traditions themselves.