I don't think strangers wrath is crossplay compatible meaning there are two different versions of the game one for ps3 and one for vita and they have to be bought seperately.
There are games that you only have to buy once and get both versions though, like sound shapes.
The purchases are tied to your account and you can use that account on 2 homeconsoles and 2 portables simultaniously. The games can be redownloaded infinitely, and systems can be disactivated from your account so if it breaks or something you can deactivate the account from it to free another systemslot for your account (I hope this makes sense).
Edit: actually i just checked Strangers wrath is not cross-buy









