Hello Pilgrim,
The answer to your question will depend on who you talk to. It is easier if one is familiar with the origin of each of these "TOC"s. That will help more than trying to approach it from a geographical/national direction.
To help you with this, there are 3 main groups to take note of;
1.) The Russian Orthodox Church Abroad (Outside of Russia) usually called ROCOR or ROCA which has recently, within the past 15 years, split into various groups usually known in shorthand with abbreviations such as ROCOR/MP, ROAC, ROCiE/V, ROCiE/A, RTOC, ROCOR-PSCA etc, which all have their own version of history and reasons why they separated.
2.) The "Florinites", named for the Metropolitan of Florina Chrysostomos (1955), who left the Orthodox Church in Greece and accepted/followed the new-calendar until 1935 when he returned to the Church and helped consecrate bishops for her. The current hierarchs of the various factions of this group all stem from ROCOR.
3.) The "Matthewites", named for Archbishop Matthew of Bresthena (+1950) who was consecrated in 1935. Those who claim to be in his lineage have also split, once in 1995 and again in 2005.
For anyone to consider joining any of these groups it is important to investigate their hierarchical lineage and Confession of faith to determine if they are the true continuation of the Orthodox Church.
This timeline will be helpful to understand the history, at least from my stand-point:
http://www.genuineorthodoxchurch.net/goctimeline.html
(others will disagree, but they can right their own post and site their own histories.) 
Oh yes, and the straight answer to the question is NO, they do not commune together except for those in the same lineage who recognize each other and have the same faith and origins.