B737-800 Captain reported a nose high left banked unusual attitude after being established in a wings level descent at approximately 25;000 feet. Aircraft had an MEL for an ADIRU that presented confusing operational limitations to the crew who made calls to maintenance and operations to clarify restrictions and requirements for Dispatch. Captain also stated a 'FLT Cont' light illuminated later in descent during Master Caution recall; but that there was no corresponding system anomaly to address. Reporter stated both ADIRU/IRSs were apparently faulty.

Narrative

Starting off ZZZ to ZZZ1 then ZZZ1 to ZZZ2 [Airports]. At ZZZ a fault in the left IRS was noted. Maintenance checked it; deferred it; then we all realized we had to switch the ADIRUs so that we can defer the right IRS instead in order to use the standby instrument per DDG (Dispatch Deviation Guide) compliance/system redundancy. DDG XY-XZ was complied with; however; there were multiple vague operational limitations such as no TOGA of flight directors. Having reading these limitations; we contacted Maintenance Control to get clarification on when; if at all the FDs (Flight Directors) can be turned on. They told us that they cannot be used for the flight; we complied. After multiple phone calls to Dispatch; Maintenance Control; and duty pilot for assistance; the flight was continued with no autopilot; FD; autothrottle; downgraded to CAT I; and we could not fly into IMC conditions due to DDG XY-XZ. This also means we flew into RVSM airspace without autopilot. Enroute; weather into ZZZ1 and our alternate; ZZZ3; went IFR; thus making us divert to ZZZ4 which was VFR. During the diversion on the descent; around FL250; the aircraft went from a wings level descent around 300 knots with speed brakes in flight detent; to a nose high/left bank unusual attitude. The FO stabilized the aircraft with slight oscillation back to a descent wings level attitude. The sensations felt like wake turbulence or mountain wave turbulence with no system failure notifications. About 5 minutes later; during master caution review recall; the FLT Cont light came on; but there were no other lights noted in the flight control panels around 16;000 ft. Crew couldn't run any checklist due to lack of failure specification from the aircraft. Crew landed safely in ZZZ4 with no further issues. Aircraft was issued AOG after further inspection from Maintenance.Cause: Overall cause was ADIRU failures in both left and right sides. Crew decided to go after consulting with Maintenance; Dispatch; duty pilot and good weather forecast.Suggestions: The obstacles that were faced on the flight risked the safety of our operation. The DDG could be more specific with how to operate the aircraft with certain limitations to help the crew make better decisions for a go/no go decision in DDG number XY-XZ.