I am confused between
I should have a place to live
I should need a place to live
Can anyone explain difference between these sentences.
Simplifying the sentences:
I have a pen (indicates possession)
I need a pen (implies that I don't have a pen, but I strongly want one)
The word "should" has a range of meanings, so your sentences are a little ambiguous, but "I should have a place to live" could express the speaker's opinion that "having a place to live" is a good thing, or desirable. This is a common meaning of "should".
"I should need a place to live" is harder to interpret with the common meaning of should, since "not having but strongly wanting" is not desirable. So it could be understood in one of the rarer meanings of "should". Perhaps this indicates a subjunctive, as in "I should need a place to live, if I were to move to Yorkshire." That is rather dated and formal, and the context may suggest a different interpretation of "should".