Sort nodes based on calculated score from CCK contents

Filter these nodes using one of the values (date)

Use the Views module. It can filter by fields.

You can postpone reading the rest of this message till you acquaint yourself with Views.

Sort the remaining nodes using a calculated value (a score, an average of several of the other values in the node)

I see two options here.

Views can only sort in the SQL level. (Well, It's possible to sort using PHP if you're not using a pager; i.e., if you have a very small number of nodes --but let's ignore this option).

One solution is to use the Computed Field module. You define, as PHP code, the value this field gets upon node submission. The drawback is that if, for some reason, you change the formula, you need to find a way to recalculate it in all existing nodes.

Another solution is to inform Views to sort by prividing the SQL formula. You do this by writing your own sort hook, or by implementing hook_views_pre_query().