Quirk was writing quite some time ago*. I think you're right in identifying 'expression' as the root of your uncertainty. It refers to more of a process than it does in current English. In that sense, 'Adverbials give expression to categories.' (So you're right about 'them' referring to 'categories'.)
PS The expression is 'Would you be so good as to...'
* PPS That Longmans book is quite recent, but it an updated edition written by other scholars. Quirk himself is in his 90s now (if he's alive).
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