The following churches are Oriental Orthodox and in communion with one another:
Coptic
Syrian
Armenian
Malankara Syrian
Indian Orthodox
Ethiopian
Eritrean
British and French Orthodox (under the Coptic, but distinct rites)
The Assyrian (Nestorian) Church is NOT Oriental Orthodox. In fact, the Oriental Orthodox is anti-Nestorian, as history shows.
The OO Church (Oriental Orthodox Church) split from the Byzantine and Roman Church (and eventually empire) for their unfair trials at and after Chalcedon. We have however maintained Orthodoxy, insomuch maintaining its Alexandrian theological thought as well, with the more advanced Severian theological thought, superior in its Christology, and have recently been realized as such by modern Chalcedonians. It is also known that the Chalcedonian Byzantines are also Orthodox as well, who were lead by great theologians like St. Maximus and St. John of Damascus. Thus, while there was a misunderstanding at the time, we have both kept the faith, and today we realize such a unity in faith.
The Oriental Church however has an diverse body of Christians. While the Eastern Orthodox have one rite, i.e. the Byzantine rite, we have a diversity of rites, maintaining another special, and very important, characteristic of the Church, i.e. to serve its people in the vernacular. This is why when you go to a Coptic or Syrian or Armenian Church, you will not find similarity in culture or the way the liturgy is sung or organized, but you will find similarity in the faith and practices of liturgy.
One important statement I must make is that we ARE NOT MONOPHYSITE. I wrote a HUGE thread on this. We are MIAphysite, or better yet, Cyrillians. Please refer to the thread "Why we are NOT Monophysites."
We are a sacramental, liturgical, traditional (following the Holy Fathers and Holy Tradition), and a loving Church, or should be. We are basically similar to the Eastern Orthodox in faith and practice, if you know about them.
God bless.
