As a dealer, how would you handle a 4-way all in on the river?

Assuming they've all shows their cards - if they haven't the answer gets more complicated:

I have shortcuts for side pots, but with that many players I'm probably not using them. Going by the book is safest. I like to narrate what I'm doing so players can follow along and check my work rather than trying to direct it themselves.

Find the best hand, count their stack, and pull that much from each player into the main. Push that to the short stack and muck their hand. Anyone with no more chips remaining, muck their hand. Repeat this process with the next best hand until there's only one hand left.

Technically, if there weren't side pots before, there are now. So you could construct them and resolve them from the outside in toward the main pot. That is what I would do with a more curious crowd and probably by default in this situation.

Narrating to the point of almost over-explaining is important for both a curious table and a yelling table. I don't move a muscle until the yelling stops though.