What could have caused these cracks, and how can I repair them?
(Caveat: I'm a DIY type, not an expert.)

Diagonal cracks in old houses are usually the result of settling. Houses start out square, but they shift over time -- and turning a square into a parallelogram means stretching one diagonal and squashing the other. I've got some of these in my house, slightly older than yours -- most were patched and repainted before I bought the place but are still visible if you look carefully, a few were probably caused when I had a loadbearing wall replaced with a parallam beam.

If the cracks are new, and you haven't done anything like I did which might cause stresses to be redistributed, you should consider getting the place inspected by a contractor and/or engineer to make sure it isn't currently moving. You may need to install lally columns in the basement, or do some foundation work, to properly support the house so it stops moving. 

Or it may be something more serious, but that's why you want the experts to look at it. (Neighbors had to demolish the old farmhouse they were hoping to rescue, when they discovered that it was both off the foundation AND had a broken main roof beam. Either would have been repairable by itself, but no reputable contractor would touch that combination.)

As far as repairing them: Once you're sure that the shifting which caused them isn't still in progress, it's like any other plaster repair. For small cracks, apply patching plaster, sand, repeat if necessary until the wall is smooth and level, and repaint. For larger cracks, you may need to use mesh tape to help support the patching plaster while it hardens. It may be desirable to undercut the crack slightly, to help ensure that the new plaster gets a good grip on the old.

If the house is going to continue to move, you're probably going to have to repair the crack repeatedly. Some folks suggest, in that case, using a paintable elastic caulk in place of the patching plaster; I'm skeptical.