What navigation publications are required when flying from KSNA to KAVX?
You'll need the navigation publications appropriate to your flight.  If you're flying under VFR, then you'll need the appropriate sectional chart, and should have airport diagrams.  You'll need to be aware of the airspace and how to communicate and navigate in it.  You should have taxi diagrams.  For VFR flying, I've always made a practice of having the appropriate terminal charts, sectionals, WAC's, and airport publications.  I have also always carried IFR enroute charts, as these provide useful information about communications enroute, as well as airspeed and navigation information.

These days, a subscription to Foreflight usually covers it, and I've flown all over using little else.  

If flying IFR, you'll need appropriate IFR publications.  

You should have a copy of the airport information, airport facility directory, or equivalent, etc.  If you don't carry and reference the current data, and end up getting busted, you'll have little to fall back on as an excuse.