How do I move my champion while the nexus is exploding?

The only way I've found to do this is using an ability that has a decent channel time right before the nexus explodes, so the channeling goes into the time where everybody stops moving. While it's channeling, I right click somewhere (anywhere should work). I've found this works best with abilities like Fizz's E, or teleport.

You continue to perform your previous command if you were untargetable at the moment that the game ended. Essentially, when the nexus explodes, it hits all targetable champions with an effect that says "stop what you are doing, stand still, and don't do anything any more."

Fizz E and Zhonya's Hourglass are the two most common ways to avoid that effect, and allow your champion to continue with the last order afterwards. I usually do this if possible, and order the champion to walk onto the enemy fountain.

I believe that Zed's ult and Guardian Angel and similar revival moves also work, but I have not tested them.