You don't have to be certified to use an oral airway. They are not considered invasive (unless things have changed significantly over the last 20 some-odd years). Similar to supporting someones broken arm in a sling. You don't need certification for that. And in fact, it takes more training and skill to properly sling an arm than to insert an oral airway. I remember teaching oral airways and bag-valve-masks in classes I used to instruct. Red Cross CPR and Basic First Aid. IIRC both of these classes were taught together, 8 hours a day for five days. Nobody ended up being certified for anything. They got a "course completion card" that I signed and gave to the students after the class was over.

I remember learning the EOA and EGTA at the EMT-Basic level, and then endotracheal intubation at the Paramedic level. These training levels do involve certification at the state level, and optional registration at the national level (I did the registrations, but IIRC it was an optional step - maybe not, I can't remember the details anymore).

[edit]Also, at the EMT-Basic and Paramedic levels you cannot "practice" on your own, you must have a "physician adviser" who takes responsibility for you. Your physician adviser determines what you can and cannot do, subject to state imposed limitations, and whether you can do these things via standing orders or require a direct order. Typically, an off-duty Paramedic can't do any of the invasive procedures unless their physician adviser is willing to go to bat and cover for them. Few would be willing to do this, in my experience.[/edit]