Obama has absolutely nothing to do with local housing authorities. His home base is Chicago, his aunt lived in Boston. He has no control over the decisions of Boston's Housing Authority decisions.
Likewise, each individual Housing Authority is under legal mandate to check the criminal records and the immigration status of their applicants. Either they failed to do so, or the information from the court that denied her assylum wasn't available for public record at the time of her application. At any rate, the responsibility for not following up on the issue belongs to the Boston Housing Authority, not Obama.
Additionaly, this was Obama's father's half sister. We already know that the relationship he has with his father's side of the family is not close. He did not have contact with his father for many years. Why would one assume that he would have close contact with his father's half sister?
Obama has spoken out on this issue since it came to light (under suspicious circumstances, to say the least). He has stated that his aunt should be subject to the same deportation procedures as anyone who is discovered to be living in this country illegally. Obviously, he has never used his political ties to insure that she be granted asylum.
The fact of the matter is, this is a matter between the woman involved and the Boston Housing Authority and the immigration courts. If Obama had stepped in and attempted to use his political influence to gain special favor for his aunt, he would have been criticised for that. The fact that he hasn't has now left him open to criticism for allowing the immigration dept. to handle their own responsibilities. If you want to criticise anyone, I'd suggest criticising the andministration currently in charge of the country that has allowed these agencies to function so inefficiently.