If default Permission levels are in place having the "Edit Page" visible in the menu already means you are Contributor which also means you should be able to Create Pages.
As "Manage Content and Structure" is visible also means that you most likely work under a Publishing Web or at least the Top-Level site is a Publishing Site. Manage content and structure would get you to a page giving you access to the "Pages" library. Try right-click or the toolbar from there which would allow creating a page.
2nd would be to append to your site Url the /Pages/Forms/AllItems.aspx - see all pages and use the "Documents" tab.
3rd would be to append to your site Url again /_layouts/CreatePage.aspx
[EDIT] - If you really want real WIKI Page, unless created in advance (either because you upgraded from Collaboration site to Publishing when activating features or by simple creating a new Wiki Page Library) you would need to create a new Wiki Page Library and you would be able to create pages directly. One similar option is also the Enterprise Wiki Site (only available with ENT License however).