You have access to all oneWorld lounges, First Class if available (AA's Flagship Lounges) and Business Class otherwise (AA's Admirals Clubs) if you are departing on a oneWorld flight on that day.
You do not have to be departing on a flight of the airline whose lounge you want to use. You don't have to be departing from the airport at which the lounge is located, so you can use it on arrival as well - subject to immigration, etc., restrictions on access to its location.
The major exception is that AA members based in North America have access to AA lounges only when they are on an itinerary that takes them outside the North American zone. Access in this case includes the points of origin of connecting flights to the international gateway, even if those flights are entirely within the North American zone.
Not every oneWorld agent at every airport knows all the rules. Have your card with you and, if possible, some documentation (perhaps a printout of the oneWorld or AA web page) to show if necessary.