If two teams end up tied in the standings at the end of the year the first tie-breaker is wins. If the Oilers and Ducks end up tied in points, the Ducks are almost certain to have more wins so that tie-breaker is almost surely lost there. The Oilers currently have one more OTL than the Predators, Jackets and Wild. They have the same number as the Blues and Stars.
If the teams are tied in wins, the next tie-breaker is the points-percentage in the season series. The Oilers have already won the season series against the Ducks (it probably won't matter) and the Blues. They lose on this tie-breaker to the Predators. If they win in regulation against the Wild they win here, if they lose, they lose here, if they win in overtime it goes to the next tie-breaker. Ties with the Jackets and Stars are set in stone.
If the teams are tied in wins and points-percentage in the season series the next tie-breaker is the goal differential on the season. Barring some crazy change to the way things are now the Oilers will lose this tie-breaker to the Jackets, Stars and Wild.
So... the Oilers hold the tie-breaker on the Blues, Stars and maybe the Wild. They've pretty much lost it to the Jackets, Ducks and Predators.