I must be subject to an ejection order (vs an eviction) if they actually want to remove me from the home.

You're probably mis-reading some of your resources. "Ejectment" is a term in some states for the removal of a tenant where there's a dispute about the ownership of real estate. In Washington, they're definitely called "eviction" lawsuits.

There is no special legal status for an adult child living in their parents home without a rental agreement; you're due the default protections of a "tenant at will" with a default 1-month term.

Removing a tenant-at-will requires first the termination of their tenancy (a private written communication between landlord and tenant) and then, if the tenant refuses to depart, a court action resulting in an order to have the tenant removed. In Washington, that final court action is a "writ of restitution".

Your parents need to give you a written notice to terminate your tenancy, and serve it to you personally (and another copy by mail, usually) more than 20 days before the start of the next rental period. A notice given today would be effective at the end of September, not the end of August.

I won't go on at length about the subsequent eviction lawsuit and procedures; you can read about them yourself, and you don't want to get an eviction on your record.

If I am locked out will I be able to contact the police to regain entry?

Yes. Keep photo ID and some evidence of your tenancy (mail addressed to you, etc) outside the house so you have access to it if you need to prove to the police that you live there.