Clustered Index and Primary Key on table with unique identifier and date
The main characteristic of the clustered index is that the data is all in that order.  That allows SQL to "read ahead".  So for example if you created your CI on the Date column and ran queries pulling summary info for a week or a month then SQL could pull the data more quickly.

If on the other hand you are having to do seeks (a single Id for example) then the CI is no different than a covering NCI.  Note the covering part of that. 

Here is something you could try.  Place your CI on the Date, OrderId combination.  Do this because you are more likely to pull range data on a date than an Id.  Also because you said that 80% of your queries use the date.  Some portion of these will presumably also use the OrderId. 

Then see what columns the queries that just use OrderId use and add those columns to an OrderId NCI using the INCLUDE clause.  And just to save time if the answer is "they are using all of the columns on these queries" then a) you need to look at those queries and see if they really need all that data and b) yes you could INCLUDE all of the columns in the table.

I realize that would be a HUGE INCLUDE.  In fact it would double the size of your table and you'll want to carefully test that you aren't going to have a serious negative impact on write operations.  However for reads it should work just fine.