Be careful of holding onto single definitions for modal verbs. These are very flexible words. Your understanding is correct, but there's much more to "should". In this case, "should be/say" refers to a coincidence or chance event. You can understand its meaning as "happen to (verb)": "It's strange that he happens to be here. He's usually on time." (I'm not sure where "here" is, in this sentence.) "I was surprised that he happened to say such a thing."

yes you've learned should correctly, the use in these examples sounds like very proper and outdated speech. It's something Sherlock Holmes would say. The first can be thought of like this: It's strange that he would think it's good to be here, He's usually on time This is a strange example because implies the speaker is somewhere he doesn't expect the subject, him, to be. for example: He wen't to the man's house to investigate, expecting the man to be at work, looked in the window to check the house is empty and was surprised to find the man to be there! he thought to himself "It's strange that he should be here. He's usually on time". for the second example it's a little like: "I was surprised that he would think it's good to say such a thing" this example is a little more self explanatory. I hope this wasn't too confusing, please feel free to ask about any of this that doesn't make sense.

"It's strange, he should be here. He's usually on time" "I was surprised, he should not have said such a thing."