OK that theme has two menus. The one in the top right corner takes it's content from Links (go to dashboard and on the left menu click Links).
The second menu, which runs horizontally below the coffee cup logo is a list of pages.
I am not sure why you have two copies of every link in the top right menu, unless you have two copies of each link in the Link list - check that.
Also, I see there is a set of theme specific tick boxes added to the bottom of each page in the dashboard editor. Select to edit one of the pages that is showing up twice in the menu and scroll down to the bottom to see if you have ticked the box to include the page in the header.