What's the difference between "take over control of" and "take control over"?

"took over control": would be like taking the task of controlling/overseeing upon oneself. "took control over": would be like bringing a situation under control which is out of control.

I think in this particular case you would need to use "of" to indicate the former e.g., take over control of the colonies.

The sentence

After the events of 1857 the Crown took over control of the Indian colonies.

is correct, because before then the territories were controlled by the East India Company.

So the sentence says that the [British] Crown took the responsibility from that company, rather than being the first party to take control. There is no duplication of prepositions:

After the events of 1857 the Crown took over / control of the Indian colonies / [from the East India Company].