The earth moves in a number of ways simultaneously.

The earth turns, of course, once per day. This rotation is actually slowing as the earth gradually becomes tidally locked with respect to the sun (much as the moon only shows one face to the Earth). This gradual process will take billions of years.

The earth also revolves around the sun (once per year) in a very slightly eliptical orbit. This rotation will also (eventually) slow and the earth will spiral into ever-closer orbits. Again, gradual, and would take billions of years or more. In fact, the sun will expand and engulf the earth five billion years from now, long before the earth has lost any noticable altitude.

Our magnetic poles do reverse from time to time. This appears to coincide with major climate changes on earth, lasting thousands of years. If this does happen, we'll have plenty of warning, and plenty of time to react.

Weird factoid: the earth is closer to the sun during what we in the northern hemisphere consider winter. It's the fact that the earth rotates slightly tilted that gives us seasons: during summer our hemisphere tilts towards the sun, getting longer days with more direct sunlight. Where'd the tilt come from? Not sure, probably an asteroid impact early in our history.

OK, here's where your 26,000 year cycle comes into play: the earth actually wobbles (like a spinning top) in a regular circular motion. it's very slight, and achingly slow, but someday we'll have a different northern star because the earth will be pointing in a slightly different direction. That's your cycle. The thing is, it's GRADUAL. It's already been going on for billions of years, and will continue to do so. It's going on right now. It's called "precession" or "precession of the equinnoxes". Absolutely no danger. It's only the accident of our north pole happening to point at a star that even made precession noticable to ancient astronomers.

If anything did suddenly make a noticable change to our axis of rotation, all the food on earth wouldn't save you-- the angular momentum of the Earth is gigantic. Any changes would likely kill most complex life on our surface and make the world permanently (ie for thousands of years) uninhabitable for any survivors.

One astronomical disaster that is worth looking at, in my opinion, is an intrasolar collison. An asteroid or comet would do unbelievable damage (depending on how big it is and how it impacts, could be a massive disaster, or the end of civilization, or the end of humanity altogether). One scenario, for example, triggers earthquakes / volcanic eruptions, drowns major oceanside population centers in unbelievable tsunamis, drenches the world in months of (initially salty) rain, starts a new Ice Age, disrupts the ionosphere (interfereing with radio) and otherwise ruins our day.

Frankly, tornados, hurricanes, train/plane/automobile crashes, heat wave-induced power interruptions, forest fires, terrorism and earthquakes are far more likely. I'd be fully prepared for these menaces before I lost sleep over anything more exotic.