Nuances in variants of “I should/would/∅ think so”

You’ve asked two different questions, or perhaps four of them.

Question the First

Unlike your second question, in this one these are all simple sentences with only one clause.

⒈ I should think so.

In complete isolation, it is impossible to say what that means.

There are two common possibilities, and many less common ones.

1. The should of obligation

It may be using should in the deontic sense of that verb, the one that means there is need or obligation, making it work like the deontic senses of these other constructions:

• I ought to think so.
• I must think so.
• I have to think so.

But I don’t believe that is what you are looking for.

2. The should of probability

The other common possibility here for should here is one of an intensifier of the belief. It means it is more probable, more likely — something rather quite expected.

The OED explains this use of should under sense 19 for shall:

19. In the apodosis of a hypothetical proposition (expressed or implied), indicating that the supposition, and therefore its consequence, is unreal.

So there is an implied protasis (conditional) here that has been omitted, and the should is occurring as it normally does (or at least, can) in the apodosis (consequent). This is less than obvious here, as the OED further explains in shall’s subsense 19d, which is own in that headword’s should section:

d. The original conditional notion is obscured in the phrases it should seem (see seem v.^{7 f}); one should think (now somewhat arch. and perh. sometimes interpreted in the sense of 18). Similarly I should think (suppose, etc.) = ‘I am inclined to think (suppose, etc.)’; also colloq. as a strong affirmation in reply to a tentative suggestion, e.g. ‘I should (rather) think he did object’.

The would of probability

So that explains the should case. And it is this second possibility of should which most likely is operative in your second sentence as well:

⒉ I would think so.

In other words, there is probably not difference between the first two in the most common cases. But you have given no context, so I cannot say for certain.

On epistemic and deontic should and would by 1^st versus 2^nd/3^rd person

For most speakers of English, the would variant is the more common. There are some speakers in southern England, however, where the should variant occurs instead. Therefore, the should version sounds a bit more formal to some people.

These are the people who use shall/should in the 1^st person and will/would in the 2^nd and 3^rd persons for the epistemic modality, and reverse those for the deontic modality. A common contrasting example-pair for that is these:

1. I shall die, no one will save me. (epistemic: a plea for help)
2. I will die, no one shall save me. (deontic: a suicide’s resolution)

Recent research has suggested that this is for the most part an invented “rule”, and that if it ever actually existed, it did so — or does so — for a tiny minority of native speakers.

So while such speakers are in a small minority, in formal writing, some publishers may still expect it. Alternately, it can be used for a deliberately archaizing effect, as occurs here:

• To be more precise, and state the matter in its simplest form, we believe that were any of the events in the previous volume of such a nature that they could be omitted without severe damage to the narrative, we should have omitted them to begin with.
  
  ―The Lord of Castle Black, by Steven Brust

There Brust is being as flowery as he can, because this is an homage to Alexander Dumas’ famed musketeers purportedly written by a stuffy professorial sort. It is supposed to sound prissily outdated and stiff as an iron rod. Don’t write like that unless you’re shooting to be similarly received.

Simple statement of belief

⒊ I think so.

This means just what it says. There is no modal involved, so no special coloring or deontic–epistemic dualities to sort out.

Question the Second

Here you give more context, so we can actually say exactly what is happening.

It is strange you should say you have seen her, seeing as she left yesterday and hasn’t been back since.

Here we have should occurring in a subordinate clause. The main clause is expressing surprise at some fact, so the should in the subordinate clause is used to denote this.

This is one of those scenarios where languages with a morphologically distinct subjunctive-mood inflection for their verbs that such forms normally occur. In English, we (tend to) use should for these situations.

The OED covers this case in sense 22c of shall down in its should section:

22. In a noun-clause (normally introduced by that).

• a. In dependence on expressions of will, desire, command, advice, request.
• b. In statements relating to the necessity, justice, propriety, etc. of something contemplated as future, or as an abstract supposition.
• c. In expressions of surprise or its absence, approval or disapproval, of some present or past fact.
• d. In clause dependent on sentence (negative, interrogative, or hypothetical) expressing possibility, probability, or expectation.
• e. In clause (now almost always with lest) expressing the object of fear or precaution.

These situations come up all the time in normal English. For example:

• Funny you should say that!