I really dislike it, sorry. Apart from being odd as a name, I also think it just sounds ugly. As a middle name it wouldn't be bad, I don't think.
Putting my dislike aside, I think it sounds good in these of your combos:
Woods Frederick
Woods Theodore
Woods Nathaniel
Woods Alexander
Woods Matthias
I think three-syllable names with the emphasis on the first syllable sound good with it, a la Woods Donovan or Woods Harrison or Woods Adrian.
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Oscar Wilde