I have never received instruction on this point, so this is just my observations and my opinion. In my small OCA parish, practically everyone stands during the Epistle reading, but a few will sometimes sit. If I am especially tired, I will choose the Epistle reading as a time to sit, but normally stand as an expression of unity of posture with the body of worshippers. I sing in the choir and read (not ordained, not usually the Epistle, mostly Hours and Psalms), so I am typically standing anyway. At Vespers, I will sometimes sit for the Old Testament reading(s) (if someone else is reading) just because I believe one *should* sit for the OT and Epistle readings. The reason I believe this is the same as the reason we should sit during the sermon, or if the life of a Saint is being read. That is the time when we are receiving instruction. Just as we would sit in a school classroom, we should sit in the classroom of the church. My perspective is probably influenced by my being a convert from Roman Catholicism, where the universal practice (at least in this country) is to sit during the OT and Epistle, but I think my opinion holds valid for Orthodox worship as well. The reason we stand during the Gospel, even though it is also instruction, is that the Gospel is in a special way "equivalent" to the Divine Logos, Jesus Christ, more so that the other parts of the Holy Scriptures. We stand then out of reverence.
On a related note, in my limited experience with OCA parishes, the general rule that the parishioners use to guide their own postures seems to be "Stand while the Royal Doors are open, sit while they are closed". However, before I joined the choir at my current parish, I would always stand during Liturgy as long as there was at least one other person standing (usually a grandmother or grandfather with iron feet). My former priest taught me that it is proper to stand regardless of whether the Doors are open or closed, and in particular it is absurd to sit during a Litany, which makes sense to me.