In addition to the other answers, I also suggest leaving a nice, polite comment letting the new user know that this behavior isn't welcome, so that we'd only need a moderator to get involved if the situation escalates. As regular users, we have the power of our words and influence to help correct the majority of issues we come across on the sites.
Most new users just need a friendly pat on the back and a "heads up" that what they're doing isn't really helpful. I make it a point to mention that, when they edit their existing posts to add more details, the post is automatically bumped to the top, so double-posting just makes it harder for the new user to get good answers. :)
This tends to work out a lot better than "HEY YOU! STOP DOUBLE POSTING OR ELSE!"
However, the other issue you mentioned that hasn't been addressed yet is the user privately contacting you. This doesn't happen to me very often, but when it does, I usually reply with something like:
I'm not 100% sure I'm the right person to answer your question, but your best bet is actually to post your question on Stack Overflow, where millions of other expert users could potentially see your question and provide answers. Since I'm just one person, I might not be able to help you as quickly as a large pool of users can.
If it is something I'm actually interested in, I might add:
If I come across your post and there are no answers, I might see if there's some information I can provide, but again, the best bet is to let the crowdsourcing powers of Stack Overflow help you.
And I also add the following:
Additionally, you should use caution when contacting users privately, many people may take offense to you reaching out to them directly, as opposed to just posting on the Q&A site. Since SO reaches the widest audience, I'd strongly suggest that over trying to contact a single user. Hope this helps!
While it seems obvious to most of us that there's more help in larger numbers, it's not obvious to everyone, and a positive message such as this may actually help modify the behavior much better than a rude response would.