Are well-known IR AAMs 'compatible' with aircraft from other countries?
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!