Could you tell me why the <th> in cloth is voiceless, but the <th> in clothes is voiced? (And indeed, why the vowel in cloth is /ɒ/, but in clothes is /əʊ/?)
The reason cloth has θ but clothes ð lies in the fact that in Old English the th in clothes was between vowel sounds. In words inherited from Old English you regularly get voiced th in this position (compare father, mother) but voiceless th elsewhere (thing, mouth, bath).
Compare north, south with θ but northern, southern with ð.
In the case of cloth-clothes it’s also part of a wider pattern in which a singular noun with a final voiceless fricative is matched with a plural with a voiced fricative: leaf — leaves, half — halves, truth truːθ — truths truːðz, house haʊs — houses ˈhaʊzɪz. You also get alternation between nouns with θ and verbs with ð: mouth maʊθ but to mouth maʊð, and sheath ʃiːθ but to sheathe ʃiːð, parallel with cloth klɒθ but to clothe kləʊð. At other places of articulation we similarly have shelf ʃelf — to shelve ʃelv, use (noun) juːs — to use juːz. (But we keep the voiceless f in to knife.)
In the OED there’s a lonɡ note at clothes explaining the history and also discussing the pronunciation with no dental fricative.