Multiple categories with common subcategories

What you could do is use a mixture of Categories and Tags if you prefer to prevent duplication of categories and confusion for the post authors.

Use the Years as categories and Blog/Announcement as tag.
So, as example:

If they post a Blog for “Year 2”, they post it in the category “Year 2” and use the tag “Blog”.
If they post an Announcement for “Year 5”, they post it in the category “Year 5” and use the tag Announcement

In your menu structure you can use a individual link / custom link with the following structure:

/%category%/?tag=%tag%

Examples:

Blog:     /?tag=blog
-Year 1:  /year-1/?tag=blog
-Year 2:  /year-2/?tag=blog
-Year 3:  /year-3/?tag=blog
...

and

Announcements: /?tag=announcement
-Year 1:       /year-1/?tag=announcement
-Year 2:       /year-2/?tag=announcement
-Year 3:       /year-3/?tag=announcement
...

Surely it depends on your permalink structure, so it could be like:

-Year 1:       /categorie/year-1/?tag=announcement

or

-Year 2:       /cat/year-2/?tag=announcement

or whatever your structure is.

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Otherwise you can create for every category-mix like
Blog & Year 1, Blog & Year 2, Announcement & Year 1, Announcement & Year 2 … a custom template file with a query calling these two categories loading into a page so you can set the page as your menu item.

Read more about queries here:

• Query_posts
• WP Query