Another Hindi nuance that is difficult to reproduce in English, unless it looks a tad awkward to a native English speaker. In the given Hindi sentence the emphasis is on the fact that Neha is saying something in English. Not on 'Neha is speaking English'; which - in Hindi - would look like "नेहा अंग्रेजी बोल रही है" i.e. drop the में to correspond with your dropping the word 'in'
I was surprised by the the last sentence in Hindi "Aamir is speaking Hindi' which was presented as - 'Aamir Hindi bhol raha hai' rather than 'Aamir Hindi mai bhol raha hai'. So it's inconsistent both that this sentence does contain the 'mai'. Possibly both are correct but it doesn't seem right that we are required to translate the 'mai' into English, where we wouldn't use it.
You mentioned there was an inconsistency. I pointed out there isn't.
When the Hindi includes "mai", then add "in" to the English.
BTW, the difference is subtle and the same that exists in English. A) His speech in English was received well. B) His English speech was received well.
Both A) and B) have almost the same meaning but subtly different. The difference is more prominently understood in Hindi, that's all. It's hard to explain, so just take it as it is.