Don't assume every example of English is perfect and standard. ;) Like Ismey59 pointed out, it's southern U.S. speech. "His" cannot work here because "his a guitar" is not a possible word-order in English (including in the dialects and slang). "Him" actually indicates "himself" (except the speaker dropped the -self).

Had HIM a guitar case is colloquial from the southern U.S.It means he had a guitar case.

I meant - He had HIS guitar case

Окау! "he had a guitar case". I understand it sentence - it easy. But I don't understand what for the word "HIM" is here.?