Greek fonts characteristically appear slanted. But they are not italic, so they don't need <i>italic</i> markup. Conversely, if a Greek word comes in the middle of an italicized passage, you do not need to close and re-open the markup around the word. Just assume the Greek matches the surrounding text.
Some books use gesperrt (spaced-out) type for emphasis within Greek passages. Mark it as <g>gesperrt</g> in the usual way.
In rare cases, books use two different Greek fonts. One will be unambiguously boldface; the other will be normal weight and probably slanted. The Project Comments should warn you. In general, mark the heavy one as <b>bold</b> and use no markup for the other one.
When you do need to use inline markup with Greek, it is best to put it outside the [Greek: ] tags, or the final text will seem to say <β>βιβλος</β>. But if this would involve a lot of extra [Greek: ] tags, the Project Comments may tell you to ignore this suggestion.
Many Greek quotations are poetry, or verse drama. There may be widely varying line lengths and indentations, and you will rarely have initial capital letters as a clue. Some line-end hyphens are intentional. If you are not absolutely certain about line breaks, ask.