Do I have to give notice? I had a shorthold tenancy agreement for 6months but it ran out 8months ago. Nothing has been said about renewing this by us or the landlord. Am I still obligated to give 30 days notice?

Tenant law goes by state. You can tell us or look it up. Most states require 30 days notice. Some of those have to be 30 days of a full rental month, others are just any 30 days. Some states have fewer - I think Florida is 15 if there is no lease.
Read your lease carefully to see if there is anything in it about tenancy after it ended.

Agree, normally all of the "terms" of the lease are still valid as a month to month rental if not renewed. So the terms to giving notice are normally accepted from the lease.

After that most ( not all) places in US require a 30 day notice even on verbal rentals.

While I don't disagree with my colleagues here. The fact is that you can tell your landlord tomorrow that you are moving out on Monday and he can't stop you. However, what he CAN do is hold you responsible for the next months rent. He can hold you responsible for the rental until the end of whatever period is required for you to give him notice. Or until he rents it to someone else.