Each of the Oaths is legendary: if you control more than one of any particular Oath, you choose one to remain on the battlefield and the others are put into your graveyard.

If you control no planeswalkers as the last ability resolves, you won’t scry at all. Abilities that trigger whenever you scry won’t trigger.

The “legend rule” checks the full names of legendary permanents. You can control Oath of Gideon and Oath of Chandra at the same time, for example.

Even if you control a particular Oath, you can cast another of that Oath to take advantage of its enters-the-battlefield ability. It will enter the battlefield, causing its first ability to trigger. You will then choose one to keep, as detailed above, and then its enters-the-battlefield ability will resolve.