My extention of stay expires January, 27 2016.My passsport expires Juli 4 2016.Immigration Office will give me a new extention of stay in January or do I need a new passport before?

Yes they will give you an extension of stay.

But only until July 4th.

You will then have to apply again with a new passport.

Get a new passport now.

As said you can apply for the extension but it will only be valid until July and you would have to apply for a new one then. Best to get a new passport.