For all sections except the first one turn off the "Different first
page" option in File | Page Setup, Layout tab.

If you don't want "Different odd and even" headers/footers, turn off
this option. (Unlike "Different first page," this option applies to
the whole document, so you'll only need to turn it off once, with the
insertion point in any section.)

Then enter the desired contents in the other headers (and/or footers).

Note that for a continous section limited to part of a page, you won't
see all headers and footers until you temporarily insert a section
break.  But if headers are linked, which they are by default, this
shouldn't be a problem for you.

For more about headers and sections, see
http://sbarnhill.mvps.org/WordFAQs/HeaderFooter.htm and
http://word.mvps.org/faqs/formatting/WorkWithSections.htm.