Just so you know, "Indo-Germanic" is an outdated and misleading name for what we now call the Indo-European group. And while there are certainly compelling structural similarities between Hindi and the Germanic languages (of which German and English are two) -- compelling to someone who knows about linguistics -- I think it's pretty far-out to suggest that they "sound alike".

Contextual language switching is a very common phenomenon. Sometimes it has to do with perceived language prestige, as anoni suggests. Switching may also occur to exclude certain listeners, of course -- that's the only kind I can recall doing myself.

People who are very fluent in two or more languages do report that they'll switch based on conversational topic, but as far as I know there are no "universals" for this. It has to do with the cultures connected to the respective languages, and the way the speaker perceived what is appropriate to each language/culture. I know nothing about LotR, but the switching you described would have seemed very clever and realistic to me.