I doubt any macro level genetic study like human genographic project has taken place in India.Small studies presents usually suffers from experimenter bias and in politically charged disciplines of humanities (history).They should be taken with a pinch of salt.moreover the genetic mapping done in genographic project has proved "Out of India" theory as baseless which also in a way makes Aryan invasion theory redundant.Aryan invasion theory even if true it would be more like "My granfather's grandfather came 500 year before your's ", rather than original inhabitants being displaced by outsiders.And if we go by later invasion of scythians,it is possible that the invasion/migration was never as cataclysmic as the proponents believe.
My opinion on the issue is that since India has a geography in which it is impregnable from three sides with one side open to anyone who wants to migrate,people at different point of time in history have migrated to India.This point could be well attested by constant stream of "Invasion/Migration" in the later part of history(Scythians,Kushans,sakas,rajputs,muslims).It is natural to believe that this has occurred earlier also.I think the only problem is that AIT is presented as something unnatural and cataclysmic.
But then i am not a historian.
Regarding languages,The fact that languages could be taught is the very fact that migration of linguistic groups could be traced.When a new group migrates into a new area,their language undergoes some change mostly to integrate new experiences they came across.They may either borrow words from existing language or coin new names for features they come across.These incremental changes lead to gradual metamorphism of a language and over a time could lead to emergence of a language which is different from the "original" one. If written record of languages is present,Comparative studies could reveal migration paths.This is the reason that in all of world languages,Nouns far outnumber verbs and adjectives.Even when they change,languages keep the integrity of verbs and adjectives (most of them need not be changed) and some basic nouns. Had languages being static,it would have been impossible to tell migration paths.
You could do a simple experiment on this forum only.
Persian language even though written in different script is phonetically similar to hindi.Some Iranian members on this forum hates dissent and are in habit of verbally abusing a member surenas.To make sure that their cuss words would not be detected by google translate,they use to write persian cusses in roman script but you would be able to easily get the meaning as they asr quite similar to the ones used in hindi (like h@rramkhor).
Bring religious epics in discussion is not bad per Se. Usually epics contain some truth in them albeit exaggerated.Troy mentioned in Homeric epics has also been unearthed in turkey.The problem only occurs when people believe timelines and grandeur ad-verbatim.