Oath of Teferi reads "You may activate the loyalty abilities of planeswalkers you control twice each turn rather than only once." my question is does this allow you to activate your loyalty abilities twice on your opponents turn as well because it states each turn rather than each of your turns? If so then that is the most broken thing ever.
No. The effect of Oath of Teferi's second ability changes only how often, not when, a player may activate a loyalty ability; it doesn't change the fact that a "player may activate a loyalty ability of a permanent they control any time they have priority and the stack is empty during a main phase of their turn" (C.R. 606.3), but not normally at any other time. Under C.R. 101.1, the effect modifies merely the phrase "but only if no player has previously activated a loyalty ability of that permanent this turn" of C.R. 606.3, and makes conforming modifications elsewhere in the rules.
If another effect allows you to use them on an opponent's turn, such as Teferi's emblem. Then the oath will allow you to activate them twice on the opponent's turn.
If another effect allows you to use them on an opponent's turn, such as Teferi's emblem. Then the oath will allow you to activate them twice on the opponent's turn.
No, it won't. Misread which effect was being used. This does work.
If another effect allows you to use them on an opponent's turn, such as Teferi's emblem. Then the oath will allow you to activate them twice on the opponent's turn.
No, it won't.
714.3. Only control of the player changes. All objects are controlled by their normal controllers.
Even if you control another player's turn, you don't control their planeswalkers, so Oath of Teferi does not apply.
-10: You get an emblem with "You may activate loyalty abilities of planeswalkers you control on any player’s turn any time you could cast an instant."
Oath only cares that something is allowing you to activate a loyalty ability. Normally, that is the normal rules of the game when it is your turn. Teferi's Emblem allows for it on the opponent's turn so Oath applies to that as well.
EDIT (Sep. 9, 2019): Edit quoted text.
No, it won't.Misread which effect was being used. This does work.Oath only cares that something is allowing you to activate a loyalty ability. Normally, that is the normal rules of the game when it is your turn. Teferi's Emblem allows for it on the opponent's turn so Oath applies to that as well.