Omitting "is", like in "I think it strange"

You might call it ellipsis, but I don't think this is the simplest analysis possible. I'd rather put to think in the category of verbs that can have an object complement, like find, consider, call, etc. The words it and strange are a red herring, non-essential.

Did she think his manners uncouth?

Do you find the house depressing?

I consider him a fool.

She called me silly.

These are all verbs that mean something like "assign label X to thing Y", but there are different verbs in this category too:

She painted the house black.

He wanted me dead.

They made me King.

I hereby pronounce you husband and wife.

In I think it strange that..., the pronoun it is used as a dummy object to refer forward to the that clause. Compare this to I don't like it that you have seduced my daughter, but so be it.

I believe this is a case of a trivalent verb. The "subject verb object" and transitive/intransitive models are really a simplification of the verb structure. It is possible for a verb to have more than two objects, in fact it is not terribly uncommon. This measure is called "valency" in linguistics.

For example:

Think!! -- Avalent
I think! -- Univalent
I think great thoughts. -- Divalent
I think it strange. -- trivalent

There are allegedly tetravalent structures in English, but I have never heard a good example, though, apparently, they are more common in other languages.

By no means is a pronoun required. For example:

I think quantum physics strange; spooky force at a distance indeed.

I will say that to my ear though, this structure (with think) sounds kind of old fashioned, or perhaps a little pretentious. But others may disagree with that assessment.