It's not entirely clear what you want, but I think you are after selecting the "best" version of each delivery address, where "best" means it has a postcode.
So, use a
row_number() over(partition by oh.Customer order by od.Postcode DESC) as [Best]
then wrap your whole query inside a subquery (or CTE) and select WHERE [Best]=1
This will give you the first address for each customer that has a Postcode - while still returning an address for those that don't have a Postcode.
If you need to prioritise between the addresses (more than one with a postcode, more than one without), just add more columns / expressions to the ORDER BY part of the ROW_NUMBER function.
Of course, this is simplistic and some validation of the Postcode may be required to make sure that a simple value of "Z" doesn't get priority over "W12 8QT"
MM
select geometry::STGeomFromWKB(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