What are some side jobs with which a mathematician in a postdoc or non-tenure-track position can make ends meet? Like many others, I did not get a tenure-track position right out of grad school. I have been moving from university to university across the US for the past few years, sometimes in the capacity of a postdoc, and sometimes in a junior (non-tenure-track) faculty position. (Many of these universities have top math departments, at varying levels; some in the top 10.)

Alas, as I move from one university to the next, my spouse is finding it harder and harder to get a full-time position each time we move. I am currently earning well, but not enough to support a spouse and kids. We're seeing our savings not-so-slowly disappear.

My question is -- what sort of "odd jobs" can someone in my position do to earn money on the side, while my spouse finds his or her bearings (yet again!) in the new location? Note that it is important that these be jobs that are sufficiently flexible that I would be able to do them while still functioning in my current university. I have excellent research (though not sufficient to have gotten a tenure-track position by now), and excellent teaching skills. While I do research in abstract Mathematics, I am also reasonably proficient in statistics and programming.

Are there natural answers to this questions that I have not thought about? Ones that are specific to people in our community? How should one go about getting these odd jobs?
Universities (especially if they're large R1 universities, almost certainly if they're in top 10) usually ask its department members whether they are willing to teach a calculus/lower-level math courses in the summer for extra pay. These are often accelerated and they are over in a couple of months. Teaching one class, in my estimate, should earn you an extra 5-10k, depending on your institution. You can easily pick up two of these classes over the summer. If there is more than one university in your area, you could also try teaching at the other universities.

You could also tutor students. This is admittedly a little awkward when you are a faculty member, but as long as you are not teaching them, there shouldn't be any problems. This works especially well in an affluent area; I'm told that some people, given good credentials, can support themselves completely on tutoring students.

Sometimes, websites dedicated to math education, such as Art of Problem Solving, hires online graders. The flexibility of the job means that you can pick it up on top of being a postdoc.

Lastly, remember that you're on a 9-month salary contract. This means that you could be an intern at some large company using your statistics/programming skills during the other three months, and earn a huge paycheck. 

These are not really "odd jobs", but probably the easiest to get given your situations. Of course, you should keep in mind that these will take away from your research time, which might make finding a tenure-track job more difficult (I totally sympathize with you; the system that we have is far from perfect, and it puts so many people in your position. But this is the reality and you should be aware of it when you're contemplating taking up another job on top of your postdoc position, which is already more than a full-time job).