The question is incorrect because it makes the wrong Presuppositions.
Why do the four verbs here (smiled, walking, shook, looking) have different tenses?
They don't have different tenses, you see. And there are five verbs in that sentence.
Smiled and shook are indeed both Past Tense, but walking and looking aren't any tense at all. Walking and looking are Participles (in both cases the Present Active Partiple, or
-ing Form, of the verb), which, like Infinitives, are not inflected for tense, or anything else.
Each of these participles heads a Participial Clause, which is usually derived ultimately from a field-stripped relative or, as in this case, adverbial clause.
- (after/while she) walked through her husband as if he were a ghost
- (as/while/at the same time she) looked him flush in the eye
They are participle clauses instead of tensed clauses because they lend a sense of immediacy and simultaneity to a description of a physical action, making the reader reconstruct the event more as a movie than a set of flat pictures. Note the alternation of the tensed and the untensed actions, like camera shots. For future analysis, this summary may be of some assistance.
As to the missed verb, it's were in the idiomatic tensed adverb clause as if he were a ghost.