Aer Lingus used to be oneworld a few years ago, but are no longer in any alliance.
Even when an airline is in an alliance they can still partner with other airlines in different alliances.
Malev (oneworld, now out of business) used to codeshare with AF/KL (SkyTeam). Malaysia Airlines (also oneworld) has a longstanding codeshare agreement with KLM as well as some Star Alliance airlines (including bmi when they existed).
Then you have Qantas that is a closer partner with Emirates than they are with airlines in their own alliance.