I'm pretty sure I've seen "da oggi" translated not literally as "from now on." Isn't this a fair interpretation? Or does it always mean literally "from today"?
I think that "da ora in poi" (from now on) and "da oggi" (from today) can be both used. It must be the same in English, I think. But "from now on" sounds more natural (even if I am Italian, and my English is far from spotless).
I think "From today" sounds a fairly unnatural in English. We'd normally say something like "Starting today" or "As of today" in this kind of context.
As of today is accepted too.
I also put as of today which has the same meaning