Adding to what Seraph said, when "enjoy" means to "to have; to possess", it is most often followed by some abstract noun such as "advantage" or "benefit":

This hotel enjoys the advantage of being near a lake that is popular with fishermen.
People who quit smoking will enjoy many benefits.
In both of the above examples, it would sound much more colloquial to replace "enjoy" with the appropriate form of "to have". (Or, for the second sentence, one could also use such verbs as "gain" or "get" or "experience," etc.)

You can also say, for instance, "I have always enjoyed good health" -- but "He enjoyed poor health" is an impossible construction, because poor health is not an advantage or benefit. (Unless, perhaps, one is trying to make a living as a beggar, as in The Life of Brian: "The leper enjoyed the extra advantage of having no legs, because passersby gave him twice as much money." But obviously that's a rather unusual and artificial example!)

From Googling, I found such phrases as обладать преимуществом ("to possess an advantage"), so that would be one context where обладать could correctly be translated as "enjoy". But, again, using "enjoy" as a synonym for "have" is rather bookish-sounding, and is only possible in certain phrases.