The evidence would indicate young Barack Hussein Obama was adopted by Indonesian citizen Lolo Soetoro after Soetoro and Obama's mother were married. The most convincing evidence is the Hawaii divorce papers filed in 1980 as Stanley Ann Soetoro vs. Lolo Soetoro. This document lists the couple as having two children. One is under the age of eighteen. That would be Maya Soetoro who was born in 1970. The other child is listed as over eighteen and in need of educational support. That would be Barry Soeroto (Barack Hussein Obama.) There are no other known children related to this marriage.
Stanly Ann Soeroto vs. Lolo Soetoro
(Click picture for larger view) PDF file here.
Another piece of evidence is Obama's Indonesian school record. This Indonesian school record has Obama using Soetoro's last name and Lolo Soetoro is listed as his father.
Barry Soetoro's Indonesian School Card
Document found here.
When Obama entered Occidental College in 1979, his mother and Lolo were still married. He appears to have registered under the name Barry Soetoro. It was at Occidental where he reverted to the name Barack Obama after his mother's divorce. We can not view his actual Occidental College records because he won't release them either.
From the Official Occidental College blog:
It was at Occidental where he stopped being called “Barry” and became Barack Obama, Newsweek pointed out in its account of Obama’s formative years that featured his black-and-white freshman photo on the cover. “It was when I made a conscious decision: I want to grow up,” he told the magazine.
This combination of evidence strongly supports the fact that Barack Hussein Obama was adopted and became an Indonesian citizen for several years.
Does this mean Barack Obama is not a natural born citizen under the Constitution? That is a difficult question. Conservative Brawler has a great analysis. You should visit his site and read the whole analysis. I have excerpted a key part below.
From Conservative Brawler:
Let's first address this from the "birther" perspective that, under older Indonesian law, Obama would have been stripped of his US citizenship after he was adopted. Since Indonesia did/does not allow dual citizenship; the United States would not recognize dual citizenship with Indonesia (since the United States only permitted dual citizenship when both countries agreed, as per the Hague Convention of 1930). Since Obama was a “natural” citizen of Indonesia after his adoption, the United States could/would not have stepped in or interfered with the laws of Indonesia. In which case, he would become solely a citizen of Indonesia and would have had to become a naturalized American citizen when returning to Hawaii several years later - thus making him a naturalized, not "natural-born" citizen and, therefore, ineligible to serve as President of the United States.
From the perspective of current law, there is no suggestion that Obama would have been stripped of his US citizenship. He would have, under section 6 (1-3) of the Indonesian citizenship law, had to issue a written denunciation to Indonesia of either his Indonesian or American nationality sometime between is 18th and 21st birthday. Did he do it? Who knows, the man won't release his records!
But let us look at the possible paths he could have taken:
a) he wrote the Indonesian authorities sometime between his 18th and 21st birthday to tell them he had chosen his American citizenship
b) he wrote the Indonesian authorities sometime between his 18th and 21st birthday to tell them he had chosen his Indonesian citizenship
c) he did nothing and, therefore, is in violation of Indonesian law
If 'a' then either Obama or Indonesia should have the records to prove it. If 'b' then, according to INA § 349, 8 USC § 1481, Obama isn't even an American citizen, let-alone "natural-born." If 'c' then he's facing a whole world of legal troubles and scandal. But let's assume he did 'a.' If he waited until he was 21 to file his papers with Indonesia, that would certainly explain the rumors about his using an Indonesian passport to get into Pakistan in 1981. That's a pretty big "if," though. And if this is what Obama did, then he and Indonesia would have the records to prove it.
If Obama was adopted in Hawaii by by Lolo Soeroto, it could explain why he won't release his original birth record. He may not be able to without a court order. The original birth certificate of an adopted person is sealed and can not be retrieved without a court order.
From Adoption Information:
Where are original birth certificates kept?
Birth certificates are usually kept at your state's Vital Records Department. An original birth certificate will be issued after when the appropriate forms are sent in by the hospital where the baby was born. If a child is adopted and an amended birth certificate is issued, the original birth certificate is stored in an inaccessible location unless a court orders the birth certificate be retrieved. (accent is mine)
If adoption by an Indonesian citizen is the reason President Obama is hiding his college and birth records, he will never willingly release them. The release would open up questions about his "natural born" status and could cause people to question his loyalty based on his time as an Indonesian citizen.