There indeed is yet another set of PIDs that are only used during GPS flight.
First set is Rate mode (inner loop)
Second set is Attitude mode (outer loop)
Several third sets are in System -> Settings -> VtolPathFollower
These should generally be tuned in order, but most normal stab tuning takes care of both inner and outer loops. Also a plug for the new version that is always about to be released (for the last 5 months anyway
) it has an autotune feature.
Also, you can get oscillations if your mags are being affected by motor current. This is usually like "toilet bowl". If the mags are really bad you can even get a fly away, so always keep an Attitude mode on your switch and PLEASE set up / test your failsafes (RC and FC) correctly even for non-GPS flight.
I recommend that you use VelocityRoam mode instead of PositionHold mode. It is the same when the stick are centered, but VR allows you to move the hold location around in very entertaining ways.
As always, start simple, and get the simple system working first, for instance get your stabilization PIDs working without GPS, then GPS and mag (mag usually green even with motors running at high power) working and tested in Basic (Complementary) before going to GPS Nav (INS13). Get VelRoam working first and without "Assisted Control" or Braking or Takeoff or Landing, etc.