In my usage, prosody is the rules of versification for the poetry of a particular language. It refers only to the poetry that actually does follow any such rules; hence, traditional verse, rather than the freer, metrically unbound poetry of the 20th century and after.
The word comes to us through Latin from Greek. It was made up of πρός, “toward,” etc., and ᾠδή, “song.” Our English word “prose” is unrelated; it has a completely Latin origin. So, don’t confuse “prose” and “prosody”!
The standard American pronunciation of the word is [ˡprɑzədi].