Differentiation of posts

I want my posts – being sorted in two categories (even and odd) – to show up in turns depending on the category they are in.

An example (let’s imagine I have 6 posts, 3 in each category):
Most recent post (odd category)
Most recent post (even category)
Older post (odd category)
Older post (even category)
Oldest post (odd category)
Oldest post (even category)

Then each category should have its color, so the code needs to be able to provide me with classes or something so I can use css on them.

Thanks in advance for your help!