The expected rise in the price of oil could
be a serious impact to industrialized nations and severely diminish the possibility to have an economy free of inflation.
(A) be a serious impact to industrialized nations and severely diminish the possibility to have - When the noun impact means the strong effect rather than a serious blow, impact if followed by "on." The noun "the possibility" is followed by either the prepositional phrase starting with "of" or by subordinate clause, and not by infinitive.
(B) seriously impact on industrialized nations and severely impede the possibility to have - "severely impede the possibility" is wrong. "impede" means to slow the progress of. We can't slow the progress of "possibility."
(C) seriously impact on industrialized nations and severely impede the possibility of having - same as B.
(D) have a serious impact on industrialized nations and severely impede the possibility to have - same as B
(E) have a serious impact on industrialized nations and severely diminish the possibility of having - ok.