What do you squawk when multiple conditions apply?
There is a trail of canceled AC's here that all say "only available within the FAA network" that might cover the topic if you can get ahold of them. 

I found a brief mentions of it in this AC relating to ADS-B and its integration with transponders. 


  Operational procedures regarding the transmission of the generic
  emergency code (i.e., 7700) in cases when the flightcrew actually
  selected a discrete emergency code (e.g., 7500, 7600);


According to that language you basically use 7700 unless its explicitly one of the other two cases. In your example I would say a hijacking supersedes all but as with many things its a case by case kind of things. 

Ultimately the codes are there as somewhat of a backup to actual radio telephony and cover 3 important cases the way I see it. In an actual scenario you use the code that is most applicable to the situation as the pilot in command sees it. 


  7500: The aircraft has been hijacked, they may not know what I (the pilot) is fiddling with so Im sending you this code since I cant say anything on the radio 
  
  7600: My radios are down, I may not be able to send or receive transmissions. There may be nothing else wrong with the aircraft in which case radio out procedures prevail. The tower may need to get a light gun out. In IMC see this question. 
  
  7700: Somethings going on this is how Im telling ATC for what ever reason chatting on the radio is insufficient. As to what the advantages are see this question.


This ICAO document on reply codes states that 


  ATS authorities should establish the procedures for the allotment of SSR codes in conformity with Regional Air Navigation agreements, taking into account other users of the system. 
  
  2.1.4.2 The following Mode A codes shall be reserved for special purposes 
  
  2.1.4.2.1 Code 7700 ... {2}7600 ... {3}7500 ... 


So what will happen when you use the code is somewhat up to local jurisdiction and you should know what will happen when you enter the code to help you (as the pilot in command) decide which one to use.