I got this question a while ago: how do you set up a document so that the page numbers go 1, 3, 5, etc.?
You take advantage of something that some people find to be a problem but can actually be used as a simple solution for exactly this situation.
If you have a right page, then you instead of doing normal flow have another right page, that skips the left page so you go 1 (no 2 from the left), 3, and so on.
Thus to have alternating odd pages, just set up your page to be Right Page Only. Choose Format > Page, Page Tab, and for the Format, select Only Right.
Click the Header or Footer tab and turn on the header or footer, and click OK. Insert your page number in either the header or footer by choosing Insert > Fields > Page Number.
Now, OpenOffice gives you the option to insert a blank page for that missing Left page. You don't want to, though. You want to make sure the phantom left (even) page doesn't show.
Choose Tools > Options > Writer > Print. Unmark the option to print automatically inserted blank pages. If you leave the option marked, then you'll get blank unnumbered pages between your odd pages.