"I assume divine names are the Hebrew ones like IHVH, ALHIM, AGLA, etc."

I've observed that people generally vibrate angelic names (Raphael, Michael, etc.), too.

"I assume divine names are the Hebrew ones like IHVH, ALHIM, AGLA, etc."

Those are Hebrew divine names. Such names exist in other languages also.

"When does one vibrate a Godname and when does one simply say it? For example, in the LBRP and its ilk, one vibrates the Names, while the Star Ruby says to roar, whisper, shout, etc. the Names."

Those are symbolic words, not necessarily literal. You can interpret them literally (changing a style of vocalization); but the main thing they do is bring your attention to the Kerub corresponding. (Roar = Lion, bellow = Bull, etc.)

"Liber V also simply requires the names to be said, but I noticed in the topic on the Star Sapphire that though it says to say ARARITA, Jim's explanation says to vibrate ARARITA. So, which is it, and when?"

If it's a Divine Name, you pretty much always vibrate it in a ritual of this sort.