I am on an understood month-to-month lease, landlord accepts my rent after 12 month lease expired.
I have found a better home, (never been comfortable here, felt like walking on egg shells) and gave notice 2 week notice only, (was I still required to give her a 30 day notice)? How does this affect my Security deposit? I am in process of cleaning the carpets.

It depends on your state.
Also, read the 'expired' lease carefully. Many are self-renewing if there is no change to rent.

Depends on where you live... the only place 15 days MIGHT be accepted is Florida...

Its at least 30 days anywhere else...

If you are countiing on that deposit before you move into the new place.. its not going to happen... the clock doesn't start ticking until AFTER you move out.. and they determine there were no damages that can legally be claimed against the deposit. But if there are none... then they have to give it back... they could legally however drag you to court for a few weeks you legally would owe... but I don't think that's likely.

Basically, you can give ONE day notice if you want. But you will be responsible for the rental until the end of the notice period. You also need to check the laws where you live. For example, some states require 30 days notice PRIOR TO THE END OF THE RENTAL PERIOD. So if the next rent is due 1/1, you might be responsible for all of January. And the landlord can apply your deposit towards that rental.

When a lease expires you become a month-to-month tenant at the same terms and conditions as the original lease except for the term. So you need to carefully read your expired lease. If the lease stated that you had to give 30 (or more) days notice that you did not intend to renew, then that time still applies even though the lease has expired.

If the lease does not say anything about giving notice then you should tell us the state where the property is located. Then we can look up the law for that state and let you know the applicable time.