I've been looking for Armenian Chant online, but while I've been able to find some, it is almost always accompanied by instruments, especially the organ. Are all Armenian Churches like this?
Organs have only been in use in the Armenian Church since the 1890's, and only sanctioned for use since the (I believe) 1920's. I can find a more definitive date, but that's what sticks out in my mind. It's common in Armenia, too, even in small village churches. If I'm not mistaken, one of the first places where organs were used in worship was in India.
As for other instruments, the only others that have liturgical use are fans with bells, cymbals, and (now quite rare) bells. If you're finding examples of "Armenian Church music" with stringed instruments and drums and such, those are just popular recordings of Church hymnography, not liturgical examples.
Also, it seems to me that the Armenian Chanting style sounds a lot more similar to Western Style chanting than even their neighbors (Georgians). Lastly, I remember someone saying that the Armenian Churches also cross themselves like the Roman Church.
I don't know about it being more "Western Style." Armenian chanting is certainly far more "Middle Eastern" sounding than you'd find in Byzantine or Western traditions, but that's just to my ears. And, yes, Armenians cross themselves left-right, not right-left.
What is the reason for these differences? What kind of contact has the Armenian Church had with the Roman Catholics? Why does it seem so different than the Georgian, Greek and Russian Churches? (obviously I realize it's an Oriental Church, but it's still in close proximity to the others)
Armenians encountered Rome through the Crusades, as well as the fact that the Armenian Church's historical territories stretched over a very, very wide territory, and took bits and pieces of things they liked into their tradition. The most obvious example being the bishop's mitre, which is identical to those worn in the Catholic Church. For most of their history, Armenians coexisted or were under the domination of other faiths and ethnic groups, so it's pretty natural that some things would find their way into usage in our church.