"Speak to him."
Translation:उससे बोलो ।
Yes in general: को marks motion towards, most often taking the place of English 'to' (but could be 'in'/'at' etc. depending on the sentence), से is literally like 'since'/'from', but also used where 'by'/'with'/'for' might be in English.
In this case @UtsavMahes is saying either can be used, I imagine the difference is the same as saying 'talking to/at' vs. 'talking with' in English, but I'm just speculating really.
I tried to wrap my head around this sentence in two ways, but neither are accepted.
Speak to him --> उसे[to him] बोलो उससे[with him] बोलो --> Speak with him
Are these translations unacceptable colloquially..? I feel I have a decent grasp on these postpositions, but this issue is challenging me.
उसे is essentially वह+को (It is also sometimes used as उसको)
उससे is वह+से
It is often very difficult to map the use of prepositions/postpositions between languages. That said, को can usually be considered similar to 'at' or 'to' while से can be considered as 'from'. In addition to this, both of them have additional uses as well.
The other use of से is that it is used as 'with' in the sense of indicating something which you are using to accomplish an action (eg: चाकू से काटना - to cut with a knife) or someone together with whom you are doing something (eg: से प्यार करना (to love with), से लड़ना (to fight with)). It is in such a way that से has been used in this sentence.
So, it might help to think of उससे बोलो or उससे बात करो as 'speak with him' (because the person you are talking is a participant in the action of speaking rather than a recipient of the action) though 'speak to him' is more natural in English.
In contrast, उसे बोलो or उसे बताओ will be 'tell him' /'say to him' because the other person is a recipient of the action rather than a participant.
[Note that this way of thinking doesn't always work. We use से प्यार करना/से नफ़रत करना even for a one-sided love/hate relationship]