Say to Somebody about Something vs Tell Somebody about Something

A) say vs tell

In general, "say" is used when describing the act of speaking itself, sometimes with direct quotes and sometime without. "Tell", on the other hand, is used to report the conveying of information. "Say" usually refers to the speech itself, while "tell", to the conceptual contents of that speech. Thus, usually, we say words/speeches but tell information/stories/the truth.

Obviously, sometimes the distinction between them is vague, and in some contexts, they can be interchangeable. For example, people might use "say the truth" and "tell the truth" for the same situation, because in casual speech, there is little difference conceptually between saying the words that represent the truth vs telling the true information.

B) "say about"

That construction is USUALLY avoided. You can say "he said something about what happened", but you can't say "he said about what happened". The reason for this is that "say" is frequently used to quote something verbatim. Obviously, in writing, you can signal a quote with quotation marks, but in speech it's harder to do, and it's generally confusing. If someone says "I said to him about something" it sounds like they are reporting the exact words spoken, i.e. "I said to him, 'About something...'". Thus this combination is avoided, both in writing and in speech.

"Say about" CAN BE used when the meaning is unambiguous. For example: "What do you say about that?" "Say, about last night..." (note: different meaning of "say" here), "Whatever you said about it must be wrong", "Say what you will about him..." In these examples, the syntax makes it apparent before you get to the word "about" that the sentence can't be interpreted as a direct quotation.

C) tell vs tell about

"About" means "on the subject of; concerning" (quote from ODO). Thus "tell me the story" is a request for the story itself, "tell me about the story" is a request for some meta-information concerning the story. Again, in casual speech, this type of conceptual difference can become ambiguous or irrelevant. There is little difference between "I told them what happened" and "I told them all about what happened." The former implies you related the whole incident, but obviously people don't regurgitate everything in photographic detail. The latter also implies that all information about the occurrence was conveyed, thus everything that the listener wants or needs to know must have been relayed. "I told them about what happened", on the other hand, is ambiguous. It could be a shorthand for "I mentioned all the relevant events" (on the assumption that I'm being cooperative), or just that I told them something about it, but not everything (if I'm deliberately waffling for whatever reason). If you want to withhold information, you could still say "I told them about it", while keeping important info to yourself. If your obfuscation is discovered, your syntax gives you some plausible deniability, and you can't be accused of telling a direct lie.

Now for your examples:

1) I said to the police about what happened: Wrong for the reason described in (B) above--it sounds like a direct quotation of an awkward sentence fragment.

2) I said to the police what happened: Wrong, also because of the reason in B) above--it sounds like "I said to the police, "What happened?"

3) I told the police about what happened: Correct. Implies you said something on the subject, but not necessarily every little detail. If your cooperation is implied in the context, it could mean that you told them everything relevant to their interest.

4) I told the police what happened: Correct. Implies you told them the exact events, or at least everything relevant/of interest to your listeners.

5) I said to the police about it. Wrong, it also sounds like a direct quote (see (B) above)

6) I said it to the police. Correct, but implies you are reporting speech/the words you said, with "it" referring to some direct quote mentioned earlier. For example: "Who did you say hello to?--I said it to the police." "I said it" doesn't answer a question like "Who did you report the incident to?" because that implies the relation of specific information, not just speaking words.

7) I told the police about it. Correct, same as (3) above.

8) I told it to the police. Correct, same as (4) above.