Final answer:
The most popular type of poem during the mid-eighteenth century neoclassical era was the heroic epic, influenced by Homer's epic poems like The Iliad and The Odyssey.
Step-by-step explanation:
The type of poem that was most popular during the mid-eighteenth century, at the height of the neoclassical era, was the heroic epic.
Homer's epic poems, such as The Iliad and The Odyssey, were celebrated during this time and served as influential models for the neoclassical poets. These epic poems had a twofold character, being both simple and "pathetic" in the case of The Iliad, and complex with recognition scenes in The Odyssey.
The heroic measure, which is a statelier and more massive form of meter, was considered the most suitable meter for epic poetry due to its ability to accommodate rare words and metaphors. Other types of poems, such as complex monologue, structured epigram, and rough-lined sonnet, were not as popular during this period.