A good way to tackle your backlog is to find ways to break it down into smaller, more manageable chunks, and just focus on those chunks. Some people already participate in something called "JRPG July", so you might decide to only play JRPGs during that month. You could also concentrate on a specific developer, and have something like "Nintendo November", for example. Or come up with some other theme that you could go with, like games that feature eggs or rabbit characters to play for the Easter period. Telling your friends what kind of games you plan on playing, and challenging them to beat more of the games that fit into the category than you do by the end of the month (or whatever time frame you agree on), can be an excellent motivator.

If you can't think of any themes, and really can't decide what you want to play next, you could just try to keep everything balanced by trying to whittle the amount of unfinished games you have for each system down to the nearest multiple of 5.

Yes, play the Vita versions. Higher resolution, more voiced lines, updated OST (or you can use the original OST if you prefer), battle fast-forward, and other improvements were made, making the Vita versions the definitive ones. All 3 Sora no Kiseki (Trails in the Sky) Evolution games have English patches, using XSeed's PC version translations. Zero no Kiseki Evolution also has a (fan translated) patch that is said to be very good. Ao no Kiseki Evolution unfortunately doesn't have a translation patch available, but I think there's one for the older PSP version.

"New: Hakuoki: Edo Blossoms (PSVita)"