Of course, I've never owned, or even ridden, any of these three bikes, but they are three of my four current choices for a replacement bike. I'm also considering a WeeStrom DL650. Here is my take based on many review on the three you've listed:
KLR - Most comfortable of the three, oldest technology (weak brakes, lame front suspension), aircooled (good and bad), most wind protection, most highway capable, large stock tank.. Everyone I know that has one has heavily modified theirs to fit there style, the aftermarket is strong, most people are not happy keeping them in stock form.
DR - small tank, feels way lighter than the KLR, more trail friendly. Less comfortable seat, small gas tank (both fixable), not nearly as much wind protection. low-tech (= good to me) and a proven cooling system without a damage prone radiator. Also has a lower seat height from what I've read.
XR (I assume you mean the L and not the R) - Much more dirtbike than the DR or KLR, more power, much less comfortable. I'm not sure what the aftermarket is like compared to the DR and KLR, but I'm sure most of it's shortcoming can be corrected as you discover them.
For back country touring, the KLR is probably the most comfortable. It's a proven platform, plenty of aftermarket, and most setup for that out of the box. I'm sure it's not that big of a deal, but the doohickey, weak brakes, suspension and the shimmed valves (plus reports of crappy brackets and rusty hardware) have me leaning away from it, but it's still a possibility. I'm looking for a bike that is dirtable (mild double track and lots of dirt/gravel roads), but not super agressive offroad, can jump on the interstate if needed, and is comfortable at 55mph. The DR can be that, if needed. All three could be that, if needed, but I've already got a smaller bike that I'm setting up for more aggressive riding, which has me coming back to the VStrom every time I think about it. A 6 speed transmission (the KLR, DR and XR are all 5 speeds) has me liking the V, and while I like simply bikes, the EFI is very reliable on the Strom. I think I would ride more with a greater variety of people than I currently do on the V as well; I tend to ride solo or with more dirt going friends mostly, but a ton of coworkers ride cruisers that I don't feel like winding my 250 out to hang with. Sorry, go off topic on your own bike choice!
Hope that helps more than it confuses!