Sorting posts using a category within a template

I want to set up a page template which diplays posts based on one category and then sorts the posts within the displayed page using either a second category or tag (ie I don’t want to sort the posts by the title, date or author).

Is it possible to do this using orderby or some other method. I’d prefer not to use a plugin if possible and I’m using 2.7

I’d be very grateful for any help with this.