So far, Livejournal is crossposting to Twitter.
Livejournal is crossposting to Facebook.
Twitter is crossposting to Facebook. (If memory serves me, this leads to a minor problem, where LJ posts turn up on Facebook both as a post in their own right, and also as a crosspost from Twitter. Minor problem, not the end of the world...)
Twitter is set up to crosspost to Livejournal, but...doesn't seem to have done so for quite some time, unless I'm missing something. Indeed, not since last December. I've just made sure the little ticky box is checked to allow such crossposting to take place (it was, so I unchecked it and checked it again). As it only crossposts in batches once a day, I don't expect that to take effect for a while.
Facebook isn't crossposting to either Livejournal or Twitter, which is a shame, because it'd be darned useful (the former, at least), but I'm not aware of any way to make it do so.
Goodreads is crossposting to Twitter and Facebook. I can't get it post to Livejournal, which is a shame, but if the Twitter crossposting thing works out, then that can kind of sort that one out.
Right, glad we got all that sorted out...