of / off / from

  1. I am finally free of dandruff.
  2. I am finally free off dandruff.
  3. I am finally free from dandruff.
    Please correct the above.

2 is incorrect.

How can we bring out the exact difference in meaning between ‘free of’ and ‘free from’?

In this example, because both work equally well, I don’t think the majority of native English speakers would consider any differences, In this instance they would use them interchangeably, as in this definition:

free from/of something not containing or affected by something harmful or unpleasant
free from difficulty/doubt/fear
free from artificial colours and flavourings
It was several weeks before he was completely free of pain.
oxfordlearnersdictionaries.c … e_1?q=free

If you really want to think things through further, then as you might imagine, there’s a great deal of discussion regarding any nuances. I think of everything I’ve read, this seems to be the clearest distinction, though it is by no means a universal agreement (I’m not sure I agree with it myself - I just provide it for your contemplation), and as I said, in the instance of ‘dandruff’ I really don’t think it matters:
“free of dandruff” gives the impression that dandruff was a burden;
“free from dandruff”, gives the impression that dandruff was in control (of your hair).

I would say that ‘free from’ suggests that certain elements/parts are not present in an entity. For example people who have an allergy will look in the supermarket shelves for food that is free from soya/gluten/wheat and so on. This really describes a state. On the other hand ‘free of’ often indicates a process of release. We could say that someone is free of cancer now having endured cancer previously. An item you buy could be free of a certain tax.

Yes, I think I get what you both mean.

But it is strangely different when we turn to their noun forms - freedom of and freedom from as is seen in:

1. You have no freedom of speech in this country.
2. You really need freedom from the Iron Curtain.

What do you say?