I agree that it would be better just to learn basic phrases in all the languages you'll encounter rather than try to master one language.
In Southeast Asia I found that communication wasn't too hard. If you're in a city frequented by backpackers, you can easily find someone who speaks a bit of English. Even if you can't, you'd be surprised how far you can get just by acting out what you're trying to say. I asked for rides, got directions, and once bought eggs in a grocery store just by miming out what I wanted. I hitchhiked countless times in Thailand and most of the time the drivers who picked me up didn't speak any English.
One thing that might be useful if you have a smartphone is to download a translation app. I didn't have a smartphone when I was there but several times when I was trying to communicate with locals who didn't speak English, they pulled out their phones and had me type what I was trying to say in English so it would translate it to Thai.
I think India is going to be the hardest place for you to communicate. I haven't been there but I've talked to travelers who have and they say it's kind of the ultimate test of your traveler prowess. I've heard that less people speak English, more people will try to scam you, and it's harder to get around. Maybe
@wizehop can drop in and give some advice based on his experiences there.
You don't need to be one of those people with their nose stuck in a Lonely Planet guidebook all the time (in fact, I would advise against it because it makes you look like a clueless tourist) but before you go, read up on common scams for the countries. Also look up what things (a meal, a taxi ride, etc.) should normally cost so you know if someone's trying to overcharge you but also know that it will happen to you and sometimes it's better just to overpay by what is really only a dollar or two rather than starting a huge argument.
If you're planning on hitchhiking,
Hitchwiki will be very useful to you. It has pages for most countries and information on how to hitchhike there. My experience in Thailand was that most people didn't understand what I was trying to do but eventually decided to help me because I was a foreigner.
Anyway, sorry to get a bit off-topic but I kept thinking of other things I wanted to say. Hope this helps!