I'm a coblogger/underling on James' blog, and in my blogging career, I've written on EOC and interacted a significant amount with EOdox. That is mostly b/c a close friend of mine with whom I grew up in the faith, after some 6 years as a Bapticostal and a student at ORU in Tulsa, converted to EOC. I was alarmed, of course, and tried to stop him, and our discussions actually for a time had me on the ropes. I was unprepared for the things he'd already thought through a few steps ahead, and so for a time I felt my own foundations shaking. Then, however, I was able to get on top of things with the help mainly of James White lectures and debates on Romanism (which is in many ways, especially in terms of authority and religious epistemology, very similar to EOC) and on Sola Scriptura, a couple of books by Eric Svendsen, and the 3-volume set "Holy Scripture: The Ground and Pillar of Our Faith" by Webster and King.
That started me down the road of being able to deconstruct the arguments that EOx put forward, and with all that behind me now, I can say with confidence (Lord willing) that EOC is totally off the table as a live option for piety toward God. My further interactions with knowledgeable EOx, both in person and in the blogosphere, both have convinced me further of the folly of EOxy and have helped me develop even more powerful arguments against it.
I'd encourage you to learn a little about EOC. A good place to start is Timothy Ware's "The Orthodox Church", but unfortunately it's a pretty sanitised version of EO theology. All the really heretical and "red flag! Danger, Will Robinson!" stuff is removed out of its presentation of EO theology, but not a bad place to start. If nothing else, someone will ask you if you've read anything, and you can tell them that. It might help satisfy them that you're not just shooting in the dark.
I've read a fair amount of "dialogue" and "conversion" stories, but most of them weren't any good, weren't helpful. Two I think would be helpful would be:
--Conversion-themed stuff written by Peter Gillquist
--My friend's conversion story
Also, I'd recommend this short e-book/long pamphlet from a Romanian who is quite familiar with EOC theology and especially the more unsavory elements and sayings from their "church fathers". I just finished reading it and recommend it because of its lengthy quotations and evaluations of what you might call "EOC's source documents" - the church writers who have gone before. Point these pagan and Platonic ideas out to those who are wavering, and if they respond with "but that's not what the Church itself believes!", ask them on what basis these same early church writers are cited sometimes to back up EOC's authority and are sometimes cast aside as "speaking only as a private theologian". It's a fatal epistemological flaw in EOC, and one that is, if nothing else, sort of fun to exploit, to watch the dancing and writhing commence.
Now, as for refuting EO assertions, I'd recommend, just like with a Romanist or a Mormon, majoring on the majors, and that would be the question of authority. I think you'll have a fairly difficult time if you try to go at it from any other position than Sola Scriptura. That is to say, the 3/4-legged stool I've heard expressed in certain Protestant contexts will not serve you well in this arena, but perhaps that's not where you're coming from.
Anyway, you can start with my recent debate on Sola Scriptura with a knowledgeable EO blogger. It's maybe not the best ever done, but I think it was quite good, it raised a lot of good issues, and it was accessible, not super super long.
In other blogging arenas, a great deal of superior material has been delivered on the Triablogue.
I am in awe of these men's abilities and output. I would encourage you not to unwisely confuse earnestness and gladness to know and be able to communicate the truth with nastiness.
My blog also has a lot of material on EOxy, so here you go:
My most fundamental recommendation would be, as I said, on the topic of authority.
Here are some posts I'd encourage you to focus on:
You'll probably also find that EOx will challenge you with "But there are so many denominations in Protestantism!" Don't let them get away with it!
The correspondent replied: I have been shocked and saddened by the number of seminarians turning Orthodox. It seems to be the cool, sentimental thing to do.
I responded: Yes, it is the cool sentimental thing to do. It's embracing "ancient" faith, "the church of the church fathers", "the early church", with liturgy and all that stuff. It looks mystically attractive. It's much more sensibly rich than a Protestant service. I can relate to the attraction. But the false Gospel, you know...sorta spoils it for me.
And that is, of course, the bottom line - does this church preach the Gospel? Does it teach that the filthy, spiritually dead, enemy of God, God-hating sinner can be reconciled to God and have peace with God by God's grace alone by repentance and faith alone in Christ alone as mediator for the forgiveness of sins? Ask any Eastern Orthodox, and make the question specific enough so as to eliminate wiggle room, and you'll find that the answer is a very clear no. Which makes the answer to the question, "Should I join this church?" pretty clear as well.