(はいたつ) Deliver like by truck or UPS or FEDEX. If you ask your friend to take a carrot to your mom next time he goes, that’s not 配達 because there’s no professionals involved and no money changes hands.
(くばる) To hand out, like fliers or tissue packets.
める(おさめる) A very narrow word:to pay taxes or to give donations to a temple.
(はこぶ) To transport – unlike 配達, 運ぶ is NOT related to business or money. If you help your friend move his fridge to his new place, that’s 運ぶ. If you pick up your suitcase and take it to the airport, that’s 運ぶ.
(ゆうそう) To send by mail.
(のうにゅう) A formal version of 配達(はいたつ). Also used to mean “pay one’s taxes.”