Can you travel to the US prior 1 months of tourist visa expiry?

No, this is definitely not true. I've had many friends travel to the States with less than 6 months to go on their visa expiration date. Also noted on the site is that the visa is valid up until the date it's set to expire. http://travel.state.gov/visa/temp/info/info_1298.html

Such an old post, sorry for such a late response. You can use your visa until the day it expires: https://travel.state.gov/content/visas/en/general/visa-expiration-date.html

I traveled with my minor son this year. His visa expiry date is 16/07/2016. We entered the USA on 25th April 2016 and came back to India on the 6th of June 2016. So I don't think its true that you cannot travel before six month or three month of expiry of passport.

Minimum validity of passport at the time of travel is 6 months. Passport expiry less than 6 months is liable to refuse entry in the country and you will be deported.
But visa validity required is minimum 3 months, as general minimum stay allowed for long term B2 visa (10 years) is 3 months.

I don't know if one has less than 3 months visa validity and on arrival ask for only 2 months or less stay, if they allow the entry or stick to minimum 3 months validity.