In Oedipus Tyrannus, should we view Oedipus as tragic only, or can we find something heroic in his actions and end?

The answer to this really depends on your working definition of "tragedy" and of "hero". Since Oedipus Tyrannos was written in ancient Greece, it makes sense to use the Aristotelian definition of tragedy and the Homeric model of the hero.

The Homeric hero is a typical figure of oral-traditional epos. Most Homeric heroes are flat and static. In other words, they have a few striking characteristics -- Nestor is wise, Odysseus clever, and Achilles...

The answer to this really depends on your working definition of "tragedy" and of "hero". Since Oedipus Tyrannos was written in ancient Greece, it makes sense to use the Aristotelian definition of tragedy and the Homeric model of the hero.

The Homeric hero is a typical figure of oral-traditional epos. Most Homeric heroes are flat and static. In other words, they have a few striking characteristics -- Nestor is wise, Odysseus clever, and Achilles strong -- but they do not have fully developed three-dimensional characters. Even though they undergo many conflicts and adventures, they rarely (with limited exceptions) display self-awareness or evolve over time as characters. One can certainly argue that Oedipus conforms to this in that his horrifying recognition of his identity is not a matter of internal psychological self-knowledge but rather simply correct apprehension of external circumstances. The unhappy ending of the play does not negate the notion of an heroic type of character; Hector was certainly a noble and heroic character in the Iliad, and yet he died and his corpse was desecrated. 

Greek tragedy is continuous with Homeric epic in the sense that most tragedies are set chronologically in the period just after the Trojan war and contain characters from the heroic age. Like heroic characters, the protagonists of tragedy are noble, and the actions in which they engage are of "a certain magnitude". Oedipus is the king of Thebes and his acts, like those of the Greek leaders during the Trojan war, have a significant impact on the lives of everyone around him. Where he differs from the traditional heroic mold is having an essential character flaw that contributes to his downfall. In other words, one could say that Oedipus, like most tragic protagonists, is a flawed hero.