As it is extremely hard to find a good online summary of all Pinyin pronunciation rules, I am listening the sounds in a Pinyin chart: https://chinese.yabla.com/chinese-pinyin-chart.php . I have read before that the final -iu is pronounced /iou/, but I can hear the "o" only in tone 3 (eg in Pinyin syllable "liu"). I am unable to hear it in tones 1 (high), 2 (rising) and 4 (falling). Is there vowel reduction in some tones or are those audios in this Pinyin chart bad?
First, it is important to distinguish between the phonemic pronunciation and the phonetic pronunciation. The first represents how native speakers interpret sounds, the latter interpret how the sounds are effectively performed.
The Pinyin final -iu is phonemically pronounced /jəu/, not /iou/ (reference: https://en.m.wikipedia.org/wiki/Standard_Chinese_phonology#Allophones). When combined with the Pinyin initial l-, that Pinyin final becomes the Pinyin syllable liu, phonemically pronounced /liəu/.
Anyway, much more important to a language learner is the phonetic pronunciation. The phonetic pronunciations of -iu may be [jəu], [jou] or even [jo̝u] (vowel O raises due to assimilation to the adjacent high sounds /j/ and /u/), which sounds similar to /ju/. The latter is the pronunciation in the audio recordings of the Pinyin syllable "liu" in the provided Pinyin table. The same also occurs in the audio recordings of the other Pinyin syllables with the final -iu.
Regarding the 3rd tone pronunciation of a Pinyin syllable with the final "-iu", when pronounced in isolation, it falls ([jo]) and then rises ([u]); in this way, this tone has an effect of separation and therefore tends to block the vowel assimilation that I mentioned before. That's why the [o] sound is heard in this tone and barely heard in the other tones in the audio recordings of the provided Pinyin table.
I don't think there is a universal rule, but rather you just have to remember it as exceptions. Even for third tone "Liu3", it could be either /liu/ (溜, as in 你中文说得很溜) or /lio/ (六).
in Chinese Pinyin, o is prounounced as wooo,so ou can never occur, because wooou is difficult to prounounce in Chinese Pinyin. Only iu is allowed.
For the case ao, actually is au, but au in handwriting is apt to be confused with an, the latter occurs very frequently in Pinyin. To be distinct to an, the pronounce au is taken over by ao.