I was writing in Latin recently and was remarking to myself how strange "proh dolor" looks. It seems odd to see a Latin word ending in "h," and a Perseus search for such words reveals (beside Semitic loanwords) only the following exclamations:
I have two questions about these words.
I believe that "h" serves simply as an expressive element. For comparison, in English expressive elements often do not fit into the normal phonetic pattern of English. For example, the glottal stop is not phonemic in normal English words, but its use in obligatory in expressions like "ouch!", "uh-oh", and "unh-uh". So also with the un-Latin use of post-vocalic H in your examples.
As for pronunciation, I see no reason why the Romans would have inserted a silent H, so these H's should be taken at face value, so proh should be pronounced [proh]. Since [h] is essentially a devoicing, one can also reanalyse [proh] as [proo̥]. You can hear something phonetically similar in a devoicing of final vowels in French, so that "vertu" can be heard as [vɛʀtyy̥] (alternatively, [vɛʀtyh].)
