Yes! All versions can now be easily jailbroken. The main features (to me) are installing KOReader to view epubs and pdf files, and hacking the screen saver display. The process only takes about an hour, mostly because you are reading, doublechecking, and downloading the right files. This guide[0] is a very good overview. I find mobileread's site to be too wordy and difficult to follow.
Which version would you buy if you were buying a Kindle today? I only owned the one before the DX... managed to crack the screen in an unfortunate elbow-related incident.
Paperwhite has been really good to me. Both Oasis and Voyage look great as well - they have higher resolution than the Paperwhite. And they have real buttons to move between pages, so if I were buying a Kindle today I'd buy one of them depending on my budget (Oasis is more expensive, but slimmer).
Current (and previous) generation Paperwhites have the same resolution as the Voyage and Oasis. I have a Paperwhite and the screen is fantastic. I'd love hardware buttons for page turning, though.
While the Oasis is expensive, if you add a nice cover to the Voyage you're close in pricing. Either go solidly midline with the Paperwhite or go all out with the Oasis, depending on your budget.
[0] http://lifehacker.com/how-to-jailbreak-your-kindle-178386407...