Kafka uses peculiar and round-about ways of saying things when talking about Gregor in order to convey the complications that Gregor's personality presents. Gregor is a man who is completely controlled by the expectations that society and his family have of him. He knows that he should work hard, be responsible, sacrifice everything for his family and be the breadwinner. These are the expectations that dominate his whole life. The reason why he is so overwhelmed by them is because these stem from his social context, and not from his personal goals or dreams.
Kafka choice of language in this passage reflects this feeling. Gregor is constantly doing what he <em>ought</em> to do, and not what he <em>wants</em> to do or what he believes in. Even when going through extremely frightening and confusing situations, he remembers that what he ought to do is remain calm. And he strives to satisfy this expectation, regardless of what his true feelings might be.
The predicate is the very and everything that follows after it, which could include adverbs, prepositional phrases, and other parts of speech. For example, "The dog ran across the street to the neighbor's house". Find the verb (the action or in your case, a linking verb such as is, are, was, wear, am). In my example, the verb is 'ran'. So the predicate is:
-ran across the street to the neighbor's house
For your sentence, the predicate is -was very strong.