The story is basically the same as the previous seasons: Dating people, who are possesed by sprits. In Difference to the previous seasons Keima, our main protagonist, has not the goal to free girls from evil sprits, but now he has to re-date the "conquered" girls to awaken goddesses who found their way into the girls along with the evil sprites. I can't really reveal the reason for that, because that would be a spoiler to a certain degree.
However, for various reasons he has a time limit of one week and the only hint to reduce the number of girls he has to re-date is that only those who remember their date, host a goddess in themselves. As the story goes on things get more complicated not only because Keima is forced to date several girls at the same avoiding to get caught, but also because problems seem to be on a larger scale due to involvements of certain groups.
In my opinion the story was never good because it is repeating. But, the main reason for this anime being a good one is the character development of Keima: from trying to adapt to his bad situation to trying to save the girls from the evil sprites and so freeing them from their unhappiness. At several points you could see how his heart was breaking, as he slowly started to feel connected to someone only to be forgotten after the date.
In this season Keima will face a much worse situation towards the end of the anime, but nevertheless he deceides to go for this route again for the greater good.
However, this anime has a major weakness: Background Story.
As some might know, Keima dated way more girls in the manga than in the anime. That would not be a problem if some of these girls were not potential goddess candidates. Somehow the anime team thought that the problem would be solved if they make an OVA only to introduce Henri/Diana and the rest can be introduced in the 1-2 min of the first episode. Former might be true, but they could have done more episodes or more OVA(sadly both cost money).
For music aspects: OST's are the same as the previous seasons and quite fitting and Opening and Ending are amazing as ever.
Side Note: It would be nice if you watch some of my anime piano covers: just insert animorypiano in youtube