As a rule of thumb, I would say most major Church Fathers before 451 would be in common between all of us, especially the ones who lived in the East. After 451, there are very few who are in common between the OO's and the Chalcedonians (EO and RC.)
I don't think that means we can't listen to EO sermons, or read some writings of post-451 EO saints. I think we just have to exercise some discretion if we are reading something that has to do with the Ecumenical Councils, since they will have a different take on that subject. On general spiritual matters that don't touch on the Councils or on Christological language, I don't see there being a problem.
Regarding St. Augustine, I've never heard him quoted or cited in the Armenian Church, but I've heard him quoted by Copts. St. John Chrysostom is definitely a saint in our Church. I hear him quoted by our priests, and some of the prayers in our liturgy are written by him. In Armenian he's called VosgePeran (Ոսկեբերան). You've probably heard him referred to by that title.
Regarding who is or is not on our calendars, there will be differences between the OO Churches, since we existed geographically isolated from each other for so long. I don't see that as a problem. I know the Copts will venerate St. Nerses Shnorhali, even if he is not on their calendar. VasnTearn has voiced the opinion that we Armenians should not venerate anyone who is not on our calendar, but I don't know of anyone else who is of that opinion. That's definitely not the view I see among Armenians in the diaspora. Perhaps in Armenia they are more strict about these things.
You may just want to ask your priest about this. If he is anything like my priest, he'll tell you to go ahead and read spiritually beneficial writings from the EO's.