In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($mathcal{F}$, $b$, ${phi}$, ${ ho}$, ${ heta}$)-sounivex functions, ($mathcal{F}$, $b$, ${phi}$, ${ ho}$, ${ heta}$)-pseudosounivex functions, and ($mathcal{F}$, $b$, ${phi}$, ${ ho}$, ${ heta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($mathcal{F}$, $b$, ${phi}$, ${ ho}$, ${ heta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.