As pointed out in that question, the differences were originally in Christology. Generally the fourth-century Christological debates were about how the relationship between the nature(s) of Christ and the person of Christ.
The "Nestorian" party held that there were two natures in Christ, the divine and the human, with very little relationship between them. Essentially there were two hypostases ("persons"), the human and the divine.
The "monophysite" party (which became the Oriental Orthodox) held that there was one nature in Jesus Christ, in which the human and the divine were brought together. Monophysitism was essentially a reaction against Nestorianism.
The remaining party is best known as the "Chalcedonian" party after the Council of Chalcedon: the Eastern Orthodox and all Western churches derive from this party. It held a view between the two: there were two natures in Christ and one person. The famous definition is the Chalcedonian definition:
in Two Natures unconfusedly, unchangeably, indivisibly, inseparably; the difference of the Natures being in no way removed because of the Union, but rather the properties of each Nature being preserved, and (both) concurring into One Person and One Hypostasis; not as though He were parted or divided into Two Persons, but One and the Self-same Son and Only-begotten God, Word, Lord, Jesus Christ
It is frequently argued that there is no substantial difference between the Chalcedonian and Monophysite positions. (It's worth noting, BTW, that the Oriental Orthodox prefer the term "Miaphysite", which essentially means the same but lacks the connotations of heresy.)
As to other theological and liturgical differences? Well, they have been divided for 1700 years or thereabouts and they grew up separately, often regarding the others as heretical. It should be no surprise, then, that they have substantial differences in liturgy and theology. All three traditions are very tradition-centred and give a special place in their theology to great theologians of the past. So the Eastern Orthodox will quote Maximus the Confessor, while the Oriental Orthodox might quote Gregory the Illuminator. But again, it's not so simple: the Armenian Orthodox (an Oriental Orthodox church) are very different from the Coptic Church (another Oriental Orthodox church) and are not in communion with one another.
The differences are complex and very old: too many to mention in this context. But if I may give an opinion as an ecumenist: the Christological differences started the divisions and dominate in ecumenical dialogue between the churches, yet they are not the reason for the modern-day division. The Oriental Orthodox and the Eastern Orthodox agreed a common statement on Christology a few years ago, but they are not in full communion because the cultural and theological divisions are too great to bridge in so short a period of time.