Which is grammatical: "it provides information on something", or, "it provides information of something", or, "it provides information about something"? Or if all are grammatical, which one is used depending on the context? Are there other prepositions possible, e.g. "in"?
First, let's take care of that pesky of.
The documents contain information of great importance.
The intercepted information was of little merit.
This doesn't speak about the subject, the actual content of the information but about the information itself: 'of questionable value', 'of no interest to me', 'of utmost urgency'. This is a rather formal, official form. Normally you'd say "important information" or "urgent information", but the of form is a well-accepted formal phrasing.
You might try to use it to indicate owner of the information, but that's really awkward. "The disk contains information of Sony on their newest mp3 player" - but I don't think you'd ever encounter it in real life. "From" or "By" will be much more natural.
Now, the subtle difference between "on" and "about". They are practically identical, with only subtle differences in rare cases. While "on" will be always information directly "on" the subject - the direct data like name, own properties, things relating directly, "about" can relate indirectly.
I have new (or, a new piece of) information about Mary: Her boyfriend was yesterday at her flat at 8PM and there was no one there, lights off, door locked, no car.
You wouldn't say information on Mary in the above example. That's indirect information, a hint, something that tells us she wasn't there then, but doesn't tell us anything directly. It sheds some light but it doesn't relate to her directly. Still, in a great many cases you can use the two interchangeably.
There's one more case when you use strictly on: Dirt. Tools of blackmail. Proofs against given person in an investigation. Compromising information.
Finally, we got some compromising information on Fisher. He called a drug dealer yesterday, and we have the call recording implying he wants to buy some drugs.
As for others...
"in"/"at" - standard locations, where the information was found. "on" can be used that way too - "I found it on the Internet!"
There's one more word that often goes with information: regarding. This is the formal counterpart to on/about, which goes in pair with of and is about the content of the information.
Information of utmost importance regarding safety of the president.