I want to move to a new place on May 1st, my contract expired in December/ 2011 I did not sign a new one, can I move with out the 30 day notice?

Not without paying for the month, you are still bound to the terms, only it is now month to month. So you would have normally either a 30 or 60 day notice provision in your paper work.

ANY question on law needs to include your general locale as laws vary by area.

Generally, if you continue to stay after your lease expires, you will be considered a periodic tenant, the period depends on the frequency of rental payments. The terms of the original lease remain in effect except for rental and term.

So you, you are responsible for giving the landlord proper notice. This doesn't mean, however, that you can't move on May 1st. You can. But it means you will still owe rent until the end of the notice period.

So lets say, the law says you have to give a calendar months notice. So you tell the landlord tomorrow that you are moving May 1 give them the May rent. You can ask for a partial refund if they are able to rent the unit before the end of May.