Adjusting the nut is the trickiest, but most important part of an action set. If the nut is too low the string will buzz against the first fret. If it is too high it can make the strings feel like a cheese cutter. And, the bottom of the slot must angle properly from front to back. If the string contact point is behind that, back in the slot somewhere, it can buzz, muffle your tone, or wreck your intonation.
Gauged files are the stated width with a half-round edge.
If you hold the file at the proper angle it will cut a perfect nut slot. The job can be done with less high tech files. Exacto makes a set of needle files available at your local hardware store. The problem of the strings rattling together could be attacked at the same time as the nut slot widening. Instead of running the file down the center of the slot, widening it evenly on both sides, file only the outside edge.