Categorize posts on a page o the basis of category of other post on the same page

I’d say you’d be looking at custom post types. Google custom post types and taxonomies and do a bit of study on that front and then you should know more about what you want to actually display. I could be misunderstanding you but doubt if categories in the blog is where to go with this, CPT’s do something similar but are much more flexible. If you work out a structure that suits you in terms of CPT’s then getting it to display how you want on whatever template pages you want is not going to be incredibly difficult, but you need to work out the structure that you use to store them in WordPress first. I would advise the Custom Post Types UI plugin as a way to play around. Then you may want to keep that or else it can give you custom code.