Unfortunately, chess960 strategy is a topic too big for a post where the primary objective is to get it finished as quickly as possible. After looking at several pages of search results for 'chess960 strategy', the most I can offer is a summary. The phrase is subject to at least four different interpretations.
Not too surprisingly, 'chess960 strategy' is often understood to mean the same as 'chess960 opening strategy'. This is partly because the main difference between traditional chess and chess960 is in the opening phase, and partly because 'opening strategy' is also a mystery for novice players of traditional chess. Here we find lists of well known opening objectives like piece development, attention to the center, and so on.
After lists of the components of opening strategy, the next step is to treat each component as a separate topic. What does 'piece development' mean when the pieces start on different squares? How does 'attention to the center' apply to specific start positions? And so on.
After considering 'chess960 strategy' applied only to the opening, the concept blossoms into principles that are valid into the middlegame and endgame. These can be extensions of the lists of opening objectives -- because they also apply throughout the game -- supplemented by lists of generic strategies that spring into action after the pieces have been developed. One example would be attacks against the castled King. Another would be maneuvers around a blocked center. And so on.
- After lists of typical, generic strategies, the next step is to examine specific strategies using concrete examples. Here we find detailed examples from real games showing 'attacks against the castled King' or 'maneuvers around a blocked center', and so on.
It looks like I've stumbled into the wrong topic for someone who is desperately short of time. It also looks like I have several ideas for future posts. Before I tackle those, I have to return to traditional chess and wade through more opening theory.