My spouse walked out 18 months ago without any form of communication until last month when he sent me a post card declaring he was going to use our son and his mother as dependents. There wasn't a return address on the post card that I could respond to. Both my son and Mother in law live with me full time. I'm I still allowed to deduct My son and MOther in Law even though he declared he was taking the Write off.

You already filed, didn't you? Check the IRS website and get the status of your return, or call the 800 number listed and talk to them. My husbands ex used his son a couple years even though he lived with us, and simply got away with it because she filed first, and rapid refunded, and we decided not to go after her for it. If he does this, you do have a way to deal with this through the IRS, but your first thing to do is go to the website and call!

Only custodial parent can claim the child. It does not count who is paying child support. Also, non-custodial parent can claim the child only if the custodial parent signs a release Form 8863 or there is a court order meeting the IRS requirements.
Read: Your U.S. Tax Return: Child of separated or divorced parents (http://taxipay.blogspot.com/2008/03/child-of-separated-or-divorced-parents.html)

Only custodial parent can claim the child. It does not count who is paying child support. Also, non-custodial parent can claim the child only if the custodial parent signs a release Form 8863 or there is a court order meeting the IRS requirements.
Read: Your U.S. Tax Return: Child of separated or divorced parents (http://taxipay.blogspot.com/2008/03/child-of-separated-or-divorced-parents.html)

Just want to clarify, I am under no obligation because I was informed he was going to claim the dependents when I can't responded back to him?

No - you are not under any obligation to notify your ex that you are claiming these people as your dependents. It might be the "right" thing to do, as a courtesy, so that he is aware if he claims them the IRS will investigate, he will lose and he will be socked by the IRS with having to pay additional taxes plus interest, but you're under no obligation to baby sit him.

One suggestion - if you both claim the same people as dependents the IRS will investigate, so you want to have documentation available that shows they live with you - items such as a school report for your son showing your address, copy of your MIL's drivers license with your address, etc.