You won't be checking in with BA at all: you must check in with the operating carrier, AA in this case. AA should have special check-in desks for oneworld elites.

Your baggage will be checked through to LAS, but you must still claim them at LAX for Customs inspection, as LAX is your U.S. airport of entry. After Customs, there should be an AA re-check desk, where you will just drop your checked baggage.

You should check with AA, but I'd be surprised if you can check your bags the night before your departure.