“deliveries order” is not right. “deliveries” by itself will probably be OK here (i.e. just delete the word “order” from your sentences).
You would not literally say “I have to finish off/up or complete all the deliveries…”, but I assume it is short for the alternatives “I have to finish off/up all the deliveries…” / “I have to complete all the deliveries…”. (It’s rather confusing to use the word “or” like this because it reads as if it is literally part of the sentence. I don’t recommend it.)