Try joining a good Toastmaster Club, this club objective is to build good english speakers. Using google try to find out if you have any club near by your place, try to pick the good one and join there.
They might ask you to pay some registration fees, let me explain you how it works, once you join there you would be given topic to present it before the audience. They will give one week time, you have the liberty to choose your own topic. When you present it, they correct it then and there and keep motivating you to do well.
Initially you will find it difficult, as you proceed with confidence, you will overcome your communication problem. I believe to develop our skills we need to be at the right place with the right people.
You will also get an opportunity to meet many people from different companies at different levels which will also help you to get into the job quickly.
Hope this helps...
I totally understand your problem and also understand you are in Kolkata. Just so you know, I run free spoken english and grooming sessions for people at my residence - a voluntary service.
If you wish to participate, you can contact me on 8697170506
People who speak English usually take years to reach a stage where they speak well.
Find people who you can talk to everyday and who can give you feedback, correct your mistakes.
If you can't find one, join a program which gives you such an opportunity.
Disclaimer: I work in a company which offers live practice based spoken English training to students all over India.