From January until the end of May, the OASDI deduction from my check was 0 dollars. Now all the sudden, as of June 2012, there is a deduction (about 5 % or so). Why is this?

Could be for a few different reasons:

1. Perhaps you aren't a US citizen and your visa status changed?
2. Or perhaps up until June you were considered a contract employee and are now a "W2" employee?
3. Or perhaps your employer made a mistake, either by not taking out OASDI prior to June or in starting to take it out now.

Obviously we can't answer your question without more specifics about your situation.