Here is what I think the Great Prophecy means
Seven half-bloods shall answer the call- Jason, Leo, Piper and 4 more half-bloods team up to defeat the giants.
To fire or storm the world must fall- Two forces (could be the Greek and Roman half bloods, Gods and Giants or Hepaestus and Zeus, or something else) Will battle for control of the world
An oath to keep with a finale breath- Possibly Chiron's oath (since he won't tell any campers what is going (Giants rising) because he swore upon the River styx not to tell what happened.) Maybe he will refuse to speak if the oath so someone kills him.(But prophecys are tricky, finale breath might not mean death.)
And foes bear arms to the doors of death- We know the Doors of Death is the opening where the most evil monsters and mortals( King Midas, Medea) are being brought back to life. But the 'foes bear arms' part is confusing, so I don't know what it means. Maybe the Greeks and Romans teaming up to destroy the Doors of Death.
This is what I think the new great prophecy might mean. Feel free to commet and let me know what you think it means.