To get SSN#'s is normally kind of difficult. I would start by tracing her name, you would be surprised how much you can find out and then sometimes come across more info, like SSN #'s too. Check into marriage certificates, if she got married, you could then find out her married name. That is public record, anyone could get that information, same with divorce records as well, and SSN#'s are usually on them too.
I'm from the Cleveland area myself, I was able to locate my bioparents as well. Feel free to send me email through my profile, I may be able to give you more tips.
Best of luck,
Robin