Can I Travel to USA from India just before 4 days before my visa expires to USA, I never Travel to USA before, but I was issued visa for 2 months, I mentioned to visa offer that I am traveling on September 10th and stay there for 15 days, yet Visa granted and visa expiring in Sept 8th, Well does it possible for me to stay in Usa for one month? and Does it effect for my future visas to usa?
You won't be allowed entry to the USA if you point of entry date is after the expiry of the visa (expired visa). If you enter before your visa expires they will give you an I-94 (electronic) and a stamp on your passport telling you when you should leave by. See Visa Expiration Dates. The visa is only for entering the USA, the I-94 is how long you can stay. The I-94 can be for much longer than your visa is valid for.
As long as you don't have an unexpired visa you should be fine, and shouldn't effect any future applications for US visas.
If your visa is expired you will need another visa, which you should get before you leave your country of permanent residence for the USA as you can't apply for one very easily outside your country of residence.
Visa Waiver Program (ESTA)
Depending on your passport and nationality you may be able to do the ESTA. See here to find if your nationality allows you to do that. If you can do that it will make things easier for you to travel to the USA.