Yes, you can have both effects apply to one enemy. Oath of Enmity does not mark the opponent.
The only spells that mark an opponent are those that explicitly say they do so. For instance, Divine Challenge explicitly states "You mark the target."
If it clears things up: marking is a condition, just like dazed, slowed and blinded are - not a kind of power. Divine Challenge isn't "a mark", it applies a mark the same way an ice spell might apply the slowed condition or a psychic attack might apply the blinded condition. Because of this, a power doesn't mark the target unless it says "the target is marked" - the same way that ice spell would say "the target is slowed". Some powers, like Divine Challenge, attach a bit extra to that marked condition, but it's still a condition.