First, "of my heart" simply means that something is associated with your emotions:
You are the love of my heart.
Also, when we use words like "heart" or "head" metaphorically, prepositions may not mean what you think they mean. Consider:
You really got in my head for a minute there.
That simply means, "You affected my thoughts," and (thankfully) has nothing to do with you shrinking and climbing into my skull.
As for "of my heart" vs. "in my heart", here's one way I might characterize the two:
- of my heart can be used with the definite article, to indicate preeminent personal feelings
- in my heart can be used with the indefinite article, to project a role
For example:
You are a diva in my heart. (means: in my heart, I regard you as a diva)
You are the diva of my heart. (means: in my heart, I regard you as the diva)
So, back to what you said:
"of my heart" sounds like you have several hearts, and one of them is your champion...
Instead:
the champion of my heart
means something more like:
there may be several people who could be my champion, but, in my heart, you are my true champion
Disclaimer: I wouldn't regard this as a hard-and-fast rule with zero exceptions. As was mentioned, prepositions are very tricky. Macmillan lists more than 20 possible usages of the word of, and when you combine those with metaphorical words such as head, heart or skin, some preposition-noun combinations will indeed be idiomatic, and need to be learned one-by-one (such as, "She really gets under my skin.")
The most basic answer to your question is that when and how they can be used all comes down to their definitions. The words "of" and "on" have quite a few variations and so there is no single right way to use them, but several.
"As to" almost always points to a decision that needs to be made, is going to be made, or can be made. It seems to always be followed by an adverb, but I am not sure whether or not that is the rule.
- I am unsure as to how we will go about this. (how to go about this is what must be decided)
- As to whether or not you won, I could not say. (The winner has not been decided)
"On" usually indicates a detailed or direct relation between the subject and its modifying prepositional phrase. Think of it like an object sitting on a table - there is direct contact.
- He gave a speech on the ramifications of not wearing protective gear while cycling. (The ramifications were the main topic of the speech he gave.)
- She was working on a solution for the global climate crisis. (The global climate crisis was the main subject of her work.)
"Of" often lends itself to less knowledge or detail on a subject on the surface, though that is not always the case.
- I have heard of him before. (I have at least a general awareness of him, but don't necessarily know much more detail.)
- Of all the cars, twenty were red. (There were twenty red cars, but specifically which ones were is left uncertain.)
"About" simply signifies a relation or subject. It can indicate great detail or a general association. Often times "of" or "on" can be used in place of "about."
- He knew many things about life and love. (He knew a good number of things about life and love. It's very general. Both of and on can be used here.)
- Her story was about the joys of sailing. (The subject of her story was the joys of sailing. Both on and of can be used here, though I feel on would work better.)
Best Answer
There won't be any simple rule we can tell you here that will tell you the right way to use words like these in every case. I can tell you this:
Most of these short prepositions have multiple meanings. The exact count will vary according to which dictionary you're looking at, but, according to this dictionary, of has 9 meanings, at has 6, with has 10, through has 10, in has 17, and on has 17 as well.
In addition to these high numbers of basic definitions, most of these words are used in idioms and phrasal verbs as well. Most people will tell you that on means “atop of” (and it does, when we say something like, the book is on the table), but, in addition to that meaning, we say things like on the radio, on the telephone, on the bus, on time, on trial, on hold, and on account of, and none of those expressions imply that anything is atop of anything else.
There are times when more than one word can be used, and the difference in meaning would be slight or negligible, such as, we had to meet Bob at the church on Oak Street (I could just as easily say, we had to meet Bob in the church on Oak Street; the latter would imply that we met inside the church, as opposed to outside in the parking lot, but, grammatically, I can still meet Bob at the church by meeting him inside the church).
When trying to determine the most common word used in an expression, Ngrams can be a good tool to use. When using Ngrams, though, be sure to look through the results as well, to find matches in contexts you might not have thought about. Such knowledge might prompt you to change your Ngram search to something more specific.