PA84 op amp instability at high(er) +/- V_s supply voltages
I won't pretend to know this specific circuit, but capacitive loads are a notoriously difficult problem for opamps...

Here is an application note describing similar stability problems and giving worked examples of solutions, which might be useful.

Edit : Reviewing the datasheet linked by Kaz, the "Stability" notes say:


  2 . Keeping the external sumpoint stray capacitance to ground at a
  minimum and the sumpoint load resistance (input and feedback resistors
  in parallel) below 500Ω. Larger sumpoint load resistance can be used
  with increased phase compensation (see 1 above).


That would be R19..21 in parallel with R5,R18 - somewhere over 2k and certainly not below 500R. Increased compensation ( increase C5, reduce R1 ) may be called for. Current values look appropriate for a gain of 30 so already on the low side for a gain of 20. 

Was someone trying to get a faster slew rate than the amp can comfortably provide? Does the application need the highest speed? If not, then just increase the compensation.

Re: supplies : the datasheet does indicate single-supply operation is acceptable, so I'm not worried about the asymmetric supply voltages. And if the -Vref supply is between 0 and -10V you should be within the common-mode input range at any setting of R45.