Oren took the Horcrux to protect it from destruction at the hands of Dumbledore's crazed followers -- both the diadem and the piece of Voldemort's soul, the former because it is a priceless historical artifact, and the latter because it does not deserve death. That much isn't supposed to be unclear -- I think I covered it way back in an earlier chapter. :) I'm pretty pleased with myself to have written enough that I can actually say things like that!
I think it gives nothing away to say that Oren wants to avoid other time-travelers like the plague, and that he has no intention of giving up the diadem if he can help it. Whether he decides to do anything in particular with it now that he's got it, beyond defaulting to waiting out the war and giving it to a museum... well, I haven't gotten that far in the story yet. :)