I wouldn't say that the purpose of the cymbals or the triangle is to enhance the liturgy (unless you think marking the rhythm of a particular hymn enhances the liturgy as a whole, somehow), though I guess others might. Honestly, at least in my own parish, we hardly use either. I don't think we've ever used the triangle (come to think of it, I don't think I've even seen one at our liturgy), and the cymbal is very sparingly used. I'm not sure what the rules are for when to use it vs. when not to use it. The last time I remember it being used is when father seemed to get frustrated with the deacons for losing the rhythm during the Hiteniyat (it sticks out in my mind because that's definitely not usual for us; everybody knows this hymn, because it's a very easy format, but I guess sometimes the melody changes and people get caught off guard).
The Byzantines are all vocal. Very occasionally you might find an organ in a Greek church, but I think such are in the minority these days (that was more popular back in the 1960s, if my record collection is anything to go by).