How do mixed-bag-of-hardware military coalitions handle communications, IFF, et. al. interoperability?
You do multinational exercises

This is a good question that was in part answered for some NATO and neighboring countries under a program called the "Partnership for Peace."  That's one of many methods various nations have used to exercise and practice interoperability, which includes figuring out the communications play.  SEATO was another regional interoperability vehicle, as is OAS.   

The first exercises I got involved with (mid-to-late 90's) were Non Combatant Evacuation Operations and Peace Keeping exercises with former Warsaw Pact countries.  It was very much a crawl, walk, jog, trot, run, sprint development model.  It doesn't happen overnight, but exercises, practice, training, and extensive military-to-military contacts go a long way toward identifying what is and what isn't interoperable.    

As to "swapping IFF boxes" that's rather pointless.  You can develop procedural control for (Return to Force)RTF procedures, and you  have to accept that in a lot of cases you can't use encrypted comms.  What you do as a group is develop a comm plan that uses generically common radio equipment (do we all have VHF? Yes? No?).  Each operation will have its own wrinkles and details.  

You build on previous multilateral operations like UN Peacekeeping

Since the UN stood up in 1945, over a hundred nations have some experience in contributing forces and equipment to UN Peace Keeping operations, and to other UN combined operations (like the UN Operations in Bosnia before 1995, or the peace keeping in the Sinai forever).  With this experience, nations have built up some "lessons learned" as a base for working with each other.   

There is no easy button; you have to do formal planning

You don't just show up with your five helicopters, say "We are here!" and get to work right away.  Your air force staff will be in contact with the other countries' air force staffs and a communications plan will be established.  A general layout for forces will be agreed, such as "who goes where?" and it takes detailed effort to establish that.  A whole host of other details get ironed out like how to get the fuel to the airfield. (See problems in Rwanda, 1994, for a prime example of the nightmare that can be).  

Military Planning, both long term and short term, is an art in and of itself. (It's painful -- been-there-done-that-got-the-t-shirt -- but it must be done).