I was having trouble to get items to respect their ordering and investigated. I found a number of posts on the net about this going back some time, so I suspect this is an unresolved issue. Anyway, this is what the issue is.

 

When you set a Joomla Menu item and select a K2 Category under 'Parameters Item Basic' you can set the 'Item Ordering" (Default, Older, Order, Most Popular etc').  However this option is only available when you select,

Layout options for multiple category selection


The consequence of this is, that if you only select a single category on the Menu Item, then there is no way to set the ordering the K2 Items on the single category. 

 

So the solution is that the option 'Item Ordering" must be available for a single category.

 

Kind Regards