Are well-known IR AAMs 'compatible' with aircraft from other countries? The AA-2 Atoll was a Russian reverse-engineered clone of the AIM-9B Sidewinder.  There are some sources that indicate, with varying degrees of veracity, that it was a good enough clone that the two could be used with the other side's aircraft (i.e. early MiGs launching Sidewinders and Western aircraft of that era launching Atolls).

However, the Russians have developed other short-range AAMs since then (Aphid, Archer), and the US has evolved the Sidewinder quite significantly from its humble roots as well.  In addition, other Western IR AAMs have been developed as well (such as the Israeli Python family).  This, along with the presence of mixed coalitions and even mixed air forces such as Malaysia's in this modern age, has me wondering: whose IR AAMs can be launched from whose planes?

More specifically:


Are current Russian jets (such as Flankers and Fulcrums) backwards compatible to the AA-2's electrical interface? (Bonus points if they can actually launch the AA-2 still.)
How backwards compatible are current Western jets (on external stores stations) to early Sidewinders, electrically speaking? (I know that some early Sidewinders required a cryobottle in the launch rail, we can ignore that for now.)
How forwards compatible are current Sidewinders to early Western jets? (i.e. could you launch an AIM-9M or an AIM-9X in analog mode off of an F-5 or A-4?)
Are other Western AAMs (such as the Israeli Python) compatible with the Sidewinder electrical interface?  (i.e. can a US F-16 hang a pair of Python-4 missiles off its wingtips and have them work "out of the box"?)
Last, and most of all, could you launch a modern Sidewinder (AIM-9L/M/P or AIM-9X in analog mode) from a Russian/Soviet jet (of any era, bonus points if it's one of the modern ones though), or have the interfaces diverged enough over the years to make that impossible?  Do the Malaysians need two stocks of IR-guided AAMs at all times, or could they get by on Sidewinders if they ran out of Archers or vice versa?
The integration of weapons in an aircraft is based on four major issues.

The first issue is the mechanical compatibility: will the airplane break when you transport or fire the missile, because the missile is too heavy and/or is too powerful?
Typically, I don't think you can fire an AMRAAM from a P-51 Mustang....
This is a huge problem, but for the examples you give, the missiles are similar to each other so there is a great chance that both Sukhoi, Mig and McDonnell Douglas fighters have enough mechanical strength to transport and fire the missile. If there is not, you cannot do a lot of things to correct it, unless you change your airplane or your missile.

The second issue is about aerodynamics: will the missile, when fired, hit the airframe? It is likely the air flow around the airframe will create whirls which that might cause the missile to be pushed into the airframe.
This issue is often solved by studying how the missile will behave in the whirls of the aircraft, and by designing it to go away from the aircraft. 
Note: you also don't want your air to air missile to go straight down, because it will lose the target. So this question of aerodynamics is always important

The third issue is about sensors: if you fire a missile, you first need to "tell" it what its target is. So you need to have sensors (or external sensors from which the aircraft has info by radio) in your aircraft.
By extension, you need to have the good sensors in your aircraft (the appropriate distance to use the full distance of the missile....). Again, for the modern fighters you mentioned, it will in general be OK. Even more if you're speaking of infrared missiles that don't have that much information before launching.

The fourth issue is electrical and electronic interfaces. In most of the cases, you can plug them in. 
But you might have to adapt the current and tension on the electrical interfaces. On that point, you are lucky because the aircraft industry uses conventions of frequency for electrical current in order to have components with the smallest weight. So there is a good chance that Russian as well as Western jets have the same frequency of currents, and can adapt the tension and current.
On the electronic interface, you might have to change the missile launcher on the aircraft to have the correct plugs. I don't know how huge is it to change a missile launcher, but I guess that if it is possible for military people to do it, it takes at least a few hours.

To conclude, there is a high probability that all the missiles you mentioned are compatible with some industrial adaptations provided to the missile and/or the missile launcher, and some programming to do in the aircraft combat system. However, combining these missiles requires that the crew doing it knows in depth both the Western jet technology and the Russian missile technology.... which might be difficult in our political reality!