Okay so I guess I can give my answer to this thread now.
Well I've first asked this same question to a few of my seniors (yes their English is pretty good ). And all of them have said the same thing as what the other members here have said i.e., your English doesn't sound weird at all just because you mix British English and American English in your speaking or writing. That's not a big deal at all, is what they have said.
But I again asked a few online friends of mine (who're native English speakers). And all of them have given a totally contrast answer to what my Indian friends have given.
Here is an extract of my conversation with one of them (his name is Flo; he grew up in UK and then at the age of 16, he went to New York for his college and since then he has been in the States i.e., for over 8 years now. So I can say he's the most apt person to answer this question).
I: Hey Flo :) How're you? I've one doubt mate!
Flo: I'm good. How's you? And what's your doubt Bro?
I: What is the difference between American English and British English. Or is there any actually?
Flo: Spelling and some grammar and some words
Lorry for truck
Colour for color
I thought you fancied her
For I thought you liked her
Personally I grew up speaking British English (Scottish really but that's a whole different can of worms) so I may be teaching you grammar that is acceptable in the UK but not in the US haha I've lived in the States long enough to be able to spell semi-properly though.
Hope that helps
I: Hey thank you. Yes it did help me and Flo I've one more doubt. Does it sound weird if we club both American English and British English? For example, if we write something like, "my favorite colour is Orange" (since favorite is American spelling and colour is British spelling), does it look odd?
Flo: Yes that is more than odd. It's also just wrong. Don't do that man. You'll get laughed at for sure. . Dude choose one or the other, or else you are incorrect in both!
Conclusion: So I can conclude that it may be okay to club British English and American English, if you're working in India. But if you go abroad (i.e., to an English speaking country), you've to take care of that. Or atleast that is what I believe so. Hit "thanks" if you agree with me (or else give your comments)