Before revision:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8 and the study for the pair (L^{\Phi,H^{\Psi})investigated in } 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{  .
After revision:  This part complements the study for the pair (H ^\Phi,L^\Psi) investigated in 8 and the study for the pair (L^{\Phi,H^{\Psi})investigated in } 19 . This paper contains new results and developments on the interplay between topology and order in Orlicz spaces that are of independent interest\emph{ . A similar analysis is carried out for the dual pair of Orlicz hearts (H^\Phi,H^\Psi) .