Answer:
A literary form in the Bible is essentially the same as in any other kind of literature in a relevant language. Examples used in the Bible include Poetry such as Psalms, Proverbs, Song of Solomon and Job. Hebrew poetry also has a number of interesting characteristics such as various types of parallelism where ideas which are similar are repeated or also opposites are put into contrast. Prose is primarily used in the other parts which primarily contain history. Although some books contain both such as the inclusion of the song of praise after the destruction of the Egyptian army in Exodus, in the middle of a historical narrative.
Jesus, as the master teacher also used a number of literary forms and devices in this work, which those who wrote down His words undoubtedly endeavored to preserve. Some of these, which are lost in translation, apparently included pnemonic devices to aid memory and note-taking (we must remember there were plenty of scribes in first century Israel, eager to record a rabbi's sayings). What we can also see is that Jesus regularly used illustrations from everyday life as an aid in memory e.g. 'Consider the lillies of the field....'
Paul also wrote a number of letters which have a definite form. They consistently follow the pattern of: 1. Salutation and introduction, 2. A Thanksgiving, 3. Main body addressing issues relating to the people addressed (this itself with a specific order relevant to the issue) 4. Conclusion and greetings.